See also Painting here.
About Teak | Preparation | Cleaning Products: | Refinishing: | Boiled Linseed Oil (BLO) vs Pure Tung oil | How to Apply Tung Oil: |

About Teak:
Teak, like many hard oily tropical woods, does not breath because the wood is saturated with a very hard yellow wax or resin. This resin creeps out of the large pours in the wood when the sun warms the wood and covers the wood to protect it from bugs, moss, mold and other stuff that might attack or damage the wood. It also turn gray after a relatively short time in the sun which is why unfinished teak wood turns gray. Mold will grow on this resin but for the most part bugs leave it alone which is why teak has been used for hundreds of years to make boats. It doesn't rot and even sea worms will not attack it. The fact that it is very hard, heavy and difficult to work with is only an inconvenience.
Source: Finishing Teakwood

One thing you have to understand about teak is the oil in teak will eventually push off any film building finish (and for that matter any finish, in fact if you read the labels of many marine finishes the don't recommend putting their products on teak). - Finishing Outdoor Teak | WoodEeb.com

Preparation:
When it comes to finishing teak wood so that it does not turn gray or black or white, there is very much information available. Unfortunately much of the information commonly available is pretty much wrong or at least self serving.
Source: Teak Finishing Blog at allguard.wordpress.com
Note: All Guard is a company which makes teak refinishing products.

The All Guard blog says,
Removing the teak resin from the surface of the teak would seem to be a relatively easy procedure and one that would be necessary for any finish to properly adhere to to the wood. And yes it should be but it is not quite that simple. Commonly used teak cleaners include sodium hydroxide (oven cleaner), sodium hypochlorite (chlorine bleach), hydrogen peroxide or a peroxide-releasing compound such as sodium perborate or sodium percarbonate. All of these products will clean the surface of the teak, but all, to some extent, etch the surface of the wood; weakening or destroying the tiny micro fibers that hold the large long fibers of the wood together. In fact, the sodium hydroxide cleaners are always accompanied by a brightener (usually oxalic acid which in its own right is a pretty good teak cleaner) to neutralize and stop the damage caused by the sodium hydroxide.

There are much less damaging products that can be used to remove the teak resin from the surface of the wood. They include the old favorite oxalic acid, trisodium phosphate (TSP), and many products commonly classified as de-greasers.

Kingsley-Bate: Elegant Outdoor Furniture recommends.
"First, hose down the furniture with fresh water. Avoid spraying the teak with a high pressure hose, as high pressure can erode the surface of the timber. Next, scrub the wet furniture using a soft bristle brush and a solution of 2/3 cup laundry detergent and 1/4 cup bleach in 1 gallon of warm water. When finished, rinse the entire piece with more fresh water to remove any remaining cleaning solution. This procedure is sufficient for general cleaning. For more difficult stains we recommend using Kingsley-Bate Teak Cleaner. This will remove the silver-gray patina and restore the furniture to a golden brown color."

BoatUS - BoatTech - Teak Care by Don Casey, says,
  "Before teak can be given any coating, it must be completely clean. Your expensive teak is literally dissolved by strong cleaners, so always use the mildest cleaner that does the job. A 75/25 mixture of liquid laundry detergent (such as Wisk) and chlorine bleach may be adequate, perhaps boosted with TSP (trisodium phosphate). Apply this mixture with a stiff brush, scrubbing lightly with the grain. Leave it on the wood for several minutes to give the detergent time to suspend the dirt and the bleach time to lighten the wood, then rinse the wood thoroughly, brushing it to clear the grain."

  If the teak is still dark or stained when it dries, a cleaner with oxalic acid is required. This is the active ingredient in most single-part teak cleaners. Wet the teak and sprinkle on the cleaner. Spread it evenly with a Scotchbrite or bronze wool pad, then give it a few minutes to work. While the wood is still wet, scrub it with the Scotchbrite pad or bronze wool. (Never, ever, ever use steel wool aboard your boat--it will leave a trail of rust freckles that will be impossible to remove.)

Tools:
Most recommend a soft bristle brush, but you can also use:
fine plastic mesh pads, Scotchbrite pads, nylon coated sponges, fine brass or bronze wool.
Amazon's recommends a plastic handle scrubber pad for a more even cleaning of the teak's surface.

Cleaning Products:

Product	Ingredients
Golden Care Teak Cleaner	Citric acid 5-10 %, Sodium Hydroxide 0-1 %, Sulfohydroxipoly Alkylether 10-15%, Oxoalcohol 5-10%	Where
Star brite Premium Teak Cleaner - STEP 1	Sodium Hydroxide (Lye), bleach, Phosphoric Acid Ester	Ace
Star brite Premium Teak Brightener - STEP 2	Oxalic acid, Alcohols, Ethylene glycol n-butyl ether *	Ace
All Guard - TeakGard® Super Cleaner	Proprietary
TE-KA Teak Wood Cleaner 2-part	Part-A: Phosphoric Acid, Part-B Sodium Hydroxide
Armada Mighty Brite Mildew Stain Remover	Sodium Percarbonate
Amazon's One-Step Teak Cleaner	Ethylene Glycol MonoButyl Ether (EGBE) *	D&R
TipTopTeak Crystal Deck Cleaner	2-Butoxyethanol, Nonplphenoxypolyoxyethanol, Sodium Dodecylbenzene Sulfonate, Sodium Metasilicate, Trisodium Phosphate

* See Acute and subchronic toxicity of ethylene glycol monobutyl ether. at the NIH
&134; Where: HD - Home Depot, Ace - Ace Hardware, D&R - D&R Boat,

About Deck Cleaning | Restore-A-Deck
Step 1. Sodium percarbonate. Step 2. Citric Acid & Oxalic acid
Mold does not thrive in acidic environments, so this is further insurance against leaving any spores in the wood.
Endorsed by East Teak Fine Hardwoods

Star brite Premium Teak Cleaner - STEP 1
MSDS (Material Safety Data Sheet) info
CAS - Chemical Abstracts Service
EINECS - European Inventory of Existing Commercial Substances

CHEMICAL NAME	CAS #	EINECS #	% w/v
Alcohol Ethoxylate	68439-46-3	Unlisted	1-4
Proprietary Acrylic Polymer Mixture			1-4
Proprietary Phosphoric Acid Ester			1-4
Sodium Hydroxide (lye, drano, oven cleaner)	1310-73-2	215-185-5	1-4
Sodium Hypochlorite (bleach)	7681-52-9	231-668-3	5-10
Water	7732-18-5	231-791-2	Balance

Star brite Premium Teak Brightener - STEP 2
Composition / Information on Ingredients

Components	CAS #	Percent
Water	7732-18-5	60-100
Oxalic acid	144-62-7	5-10
Alcohols, C9-C11, exthoxylated	68439-46-3	1-5
Ethylene glycol n-butyl ether	111-76-2	1-5

Composition comments All concentrations are in percent by weight unless ingredient is a gas. Gas concentrations are in percent by volume.

Refinishing:
Summary of finishes:
Oil:
Oxidize over time. The oxidization of surface oils causes teak wood to appear weathered or gray.
Can cause mildew or irregular coloring.
Restores natural oil in the wood.
Teak Care at McGill Teak furniture says,
90% of our customers like the warm feeling of teak Patio furniture with Teak oil rather than Teak Protector, but again its a very hard earned choice.

Water Based:
Lasts longer. up to 4 times
Easy to apply.

Products:
Most Teak Oil and Tung Oil you get a hardware stores are oil/varnish/mineral spirit blends (wiping varnish) with only small amounts of the named oil mixed with other oils. The only place I could find pure tung oil was mail order and a boat dealer.
The marketing guys at manufacturers started naming things like Danish oil, Teak Oil, ... but usually don't list the ingredients on the can. Even the Material Safety Data Sheet (MSDS) list only the thinner, because the oil itself is not a dangerous substance (I guess).
See:
Boiled Linseed Oil (BLO) vs Tung Oil
Oil Finishes: Their History and Use | Popular Woodworking Magazine
rec.crafts.woodturning

Name	Description
Pure Tung oil	Not available in Home Depot, Lowes, Ace, ... Mail order at Woodcraft.com, Real Milk Paint and Woodworkers Supply (woodworker.com). I found some at my boat dealer.
TeakGuard	A water based acrylic polymer resin mixed with UV reflective materials that contains no oil, urethane, silicon, varnish, shellac, or sealers of any kind. See How Is TeakGuard Different?
Daly's SeaFin Teak Oil®	A Tung Oil finish that is widely available in the Northwest. Tung, Phenolic, Oil Modified Urethane
Waterlox®	A nationally available Tung Oil product that is similar to Sea-Fin. It is generally available only through the mail-order catalogs.
Watco Teak Oil	Watco® Teak Oil Finish, in the can with the blue label. While it is a Linseed Oil finish with UV inhibitors added, its finishing properties are considerably different from the more familiar Watco Danish Oil.
Cabot Australian Timber Oil (ATO)	Recommended in several places.
Watco Danish Oil	An oil (only) finish that is made from linseed, soybean, and other oils, a lot of thinner, and no varnish resins. Since they contain no varnish resins, Danish Oils will not build a surface film, and any film that will form is incidental to the amount of linseed oil that is present. While Danish Oils are fast and easy to apply and have many other uses for our finishing, they are not a good final finish for our turned wood. The finish is soft, not very durable, and will require rejuvenation every couple years when exposed to even indirect sunlight.
DIY	I use a mixture of equal parts 100% pure Tung Oil, Varnish, and Turpentine. Russ's Corner: A WoodCentral Archive
Minwax Tung Oil Finish & Formby's Tung Oil Finish	Oil/Varnish blend - Mineral Spirits (65% Minwax, 78% Formby's)
Sikkens Cetol Oil	A varnish with pigments and other additives. Can produce an orange-ish somewhat opaque cast.

Sources:
Russ's Corner: A WoodCentral Archive

Boiled Linseed Oil (BLO) vs Pure Tung oil

BLO	Pure Tung oil
Has added metal compounds	Pure
Dries faster (because of added compounds)	Dries more slowly
Will yellow with age	Doesn't yellow
Can go rancid	Nope
Can mildew	Nope
Nope	Has waterproofing qualities
Nope	Retains some flexibility when hardened
Cheaper	More expensive

Source: Tung oil Debunking the myths

How to Apply Tung Oil:
Formby's directions:

1. Surface should be thoroughly cleaned. Remove any dirt or wax build-up before applying Formby's(R) Tung Oil Finish.
2. Put a small amount of Tung Oil Finish on a Formby's(R) Finish Applicator Pad or a soft, lint-free cloth and rub into the wood. For best results apply a thin coat and work the Tung Oil into the wood surface, similar to the way you would wax a car.
3. Tung Oil should dry within 12 hours. Buff lightly with a very fine steel wool pads. Wipe thoroughly with a soft, lint-free cloth. Rub in a second coat. To build sheen and add protection, additional coats may be applied.

Oil Finishes: Their History and Use | Popular Woodworking Magazine:
Wipe, brush or spray the finish onto the wood; keep the wood wet with the finish for 5 to 10 minutes, or until it stops soaking in; then wipe off the excess and allow the finish to cure overnight at room temperature. Sand tung oil after every coat, not just after the first, and it takes five to seven coats, allowing two to three days drying time between each, to achieve a smooth, attractive sheen.

Tips for Using Pure Tung Oil: A Beginner's Guide | Real Milk Paint Co.

1. Clean the surface

The proper application of tung oil depends on you starting with a clean and properly prepared surface. Before you start, make sure there’s no grease, oil, dirt, dust, or other contaminants on the surface.

If necessary, start by sanding or stripping the surface to remove any coating or finish that's already there. Tung oil can only be applied to bare surfaces or over another coat of tung oil. Follow that up by cleaning the surface with trisodium phosphate. Sand the surface one more time with 150-grit sandpaper, and then vacuum well to remove all dust.

2. Thin the oil

A thinner will make the tung oil easier to apply and faster to dry and will improve penetration. The only time you shouldn't thin the oil first is if you're applying it to weathered wood, concrete, old and unfinished wood floors, or other highly absorbent surfaces. To thin the oil, combine it with equal parts Citrus Solvent , mineral spirits, or Odorless Mineral Spirits before application. Or choose one of our pre-thinned options, Half & Half or Dark Half, to use straight out of the bottle!

3. Apply a generous first layer

You can apply the oil with a natural bristle brush, a sponge brush, or a soft and lint-free rag. Apply the oil liberally to the surface. Unlike varnish (which sits on top of the wood), the goal with tung oil is to thoroughly saturate the wood cells. When you've applied the first coat, let the oil absorb.

4. Apply subsequent coats

After the first coat has absorbed, apply a second coat. Continue this process of applying coats until over 80 percent of the surface stays glossy for at least 40 minutes. This means the wood cells have been saturated. Decorative items may need two to four coats, while functional surfaces that will be handled, used, or walked on will need a minimum of three to five.

5. Allow the oil to soak in overnight, and repeat the next day

When the wood won't absorb any more oil, use a clean rag to wipe the surface. If there are any puddles of oil on the surface, mop them up with the rags.

Leave the tung oil to fully soak into the surface over the next 24-hours, or until there’s a consistent sheen over the entire surface. This process could actually take up to 48 hours. Then, apply one to two more coats as before, waiting at least 40 minutes for it to soak in. When the surface is glossy, wipe up the excess with a rag. Hang wet rags to dry before disposal.

6. Let the oil cure for up to 30 days

From here, the oil will need a week to 10 days to start curing, and 15 days to 30 days to fully cure. Do not put the tung oiled object in direct sunlight for an extended period of time. During this curing time, you can walk on floors with clean shoes, but avoid placing heavy objects on the floor or walking on it with dirty shoes. There is no other sealers or protective products needed on top of your oil. It naturally seals, waterproofs, and protects your surfaces!

7. Cleaning your surfaces

Pure tung oil is easy to clean! For your floors or other wooden objects, just simply use hot water and standard dish soap. Thats it!

8. Reapply as necessary to revive and provide more protection

Surfaces that are used often or walked on frequently may need some maintenance \1" TARGET="_blank">to revive their look and add more protection. To do this, simply mix 2 parts thinner to 1 part tung oil and wipe down your surfaces. Allow time to dry as necessary.

Tung oil has been popular for thousands of years, thanks to the protective and waterproof finish it creates on wood and other porous surfaces. These days, pure tung oil is also gaining momentum because it's non-toxic, environmentally friendly, and food safe, meaning it's ideal for kitchenware, butcher block, cutting boards, countertops, and even toys!

Tung oil is just like linseed oil or oil/varnish blend, but you have to sand tung oil after every coat, not just after the first, and it takes five to seven coats, allowing two to three days drying time between each, to achieve a smooth, attractive sheen.

Thining Tung oil - can I use any paint thinner?: Prashun Patel wrote,
  You CAN thin tung oil with turpentine or mineral spirits, but you certainly don't HAVE to. If I were you, I would not thin it; apply it raw and neat.
  If you find it too thick to rub around on a broad surface, then instead of thinning, I would heat it gently (which will reduce the viscosity temporarily) and apply it warm.
  Don't be wooed by the 'if you thin it it penetrates deeper' theory. Oil doesn't need to penetrate that deeply to serve its purpose: mild protection.

James Owen's wrote:
  Depending on heat and humidity, pure tung oil is normally "dry" in 24 to 48 hours during warm months....during cooler weather it can take up to a week or more.....   Once it is dry to the touch (~ 24 hours or so -- see above), you can add another coat.
If you are not already aware of this, you might be interested to know that tung (and boiled linseed) oil is a drying oil, meaning that it cures by chemical reaction with the oxygen in the air to form a long-chain polymer. Cure time for tung oil (and real boiled linseed oil -- not the stuff with lots of chemical driers) is around 35 to 40 days. And a bonus with both pure tung oil and Boiled Linseed Oil without the extra chemicals is that, once cured, it is food safe......

Safety note: because tung/linseed combines with oxygen to cure, it releases heat in the process....so make sure that you lay your oil-soaked rags out flat on a non-combustable surface like your concrete garage floor, where there is plenty of air circulation, until they are dry, or put them in a bucket of water.

My brother uses lacquer thinner instead of turpentine because it is more volatile and will dry faster.

Tung Oil - Woodwork Details says,
You can thin the first coat of tung oil 50/50 with turpentine for better penetration, but put subsequent coats on straight. Comments at WoodenBoat.com Forum
I've used Watco Teak Oil. Not super impressed. I much prefer Daly's SeaFin Teak Oil.

The finishing experts class Watco Danish Oil, Homer Formeby's "Tung Oil", Seafin, et al as "wiping varnishes", which is to say that they are a mixture of varnish, a lot of solvent and possibly some oil, usually with some japan drier tossed in for flavor.

See About oil wood finishes in the painting page.

Teak Care by Don Casey says,
Apply an oil wait two weeks then apply a sealer.

Oils known as teak oil are predominantly either Tung oil or linseed oil that are fortified with resins to increase durability. The linseed-based oils are usually less costly, but they may darken the teak. Tung oil-based products are less likely to darken the wood and are often more water-resistant. Oiling can take several coats to bring the wood to a non-shiny matte finish. Unfortunately, the effect of oiling --- while it does restore the glow and return natural resins to the wood --- does not last. Within a month or two, regardless of which oil was used, the oils will carbonize and the teak wood is probably destined to turn dark again.
Source: Teak Wood Restoration Explanation | Home Guides | SF Gate

Sealing Finishes:
The problem with these finished that form water tight seals is that there is always a small amount of water absorbed into the surface of the teak. When the Sun shines on the wood some of the water vaporizes and tries to expands to many times its original volume.
Eventually these pockets turn into blisters and when they get big enough and the finish becomes brittle enough, the blister cracks.
Source: Finishing Teakwood | Teak Finishing

"Kingsley-Bate does not recommend oiling teak furniture or the use of oil based products. If done improperly, oiling can cause mildew or irregular coloring and is not covered under warranty."

Wood Finishing & Refinishing at UtahState says,
  One of the newest and most unusual finishes available today is the penetrating resin finish. As the name indicates, resins are added to penetrating oils. When these resins penetrate into the wood, they become extremely strong and hard and are very resistant to water, alcohol, heat, and abrasion.
Penetrating resins are self-sealing.
  Open grain woods such as oak, teak, and mahogany will take a penetrating resign well. However, you'll probably have to give these woods at least three applications to fill the open grain structure.

Finishing Outdoor Teak at woodweb.com comments:
If you're looking for something that will be easy to service, user friendly, and hold up to the elements, Cetol Oil would be a good choice. Akzo Nobel makes a product called Sikkens Cetol Oil in gloss and satin. It can be brush applied and it holds up quite well. You can find it at most marine supply stores.

Teak Care & Preservation at Marine Development & Research (MDR) says,
  "There are a couple of ways to increase the longevity of teaks beautiful golden color. One is to apply at least 3 coats of a quality teak oil like Amazon's Golden Teak Oil following the instructions on the label. The second is the application of Amazon's TEAK LUSTER. This new product is a clear WATER BASED acrylic coating that actually allows the wood to breath. It has 94% UV blockers to keep the teak looking great for up to 3 YEARS.
  Tt is important to get the oil as deep as possible into the wood. This can be accomplished by mixing some of the remaining "Teak Prep" used in the last step with the oil in a ration of 25% "Teak Prep" to 75% teak oil. This formulation should be used for the first two coats with the third and final coat being 100% oil.
  The correct method to apply oil is by hand. wiping the wood with a rag saturated in oil with the grain, which helps 'squeegee' the oil into the wood. Let stand for approximately fifteen minutes. This allows the wood to absorb as much oil as possible. Then wipe off the excess oil with a clean DRY rag. If this step is not completed, the oil will begin to cure on the surface, becoming sticky, and may never dry properly.

Teak Care at McGill Teak Furnature says,
  Application of Teak Oil needs more maintainence (about twice a year depending upon the area), and teak protector need application about once a year. 90% of our customers like the warm feeling of teak Patio furniture with Teak oil rather than Teak Protector, but again its a very hard earned choice.
  McGill Teak protector. This is a water-based treatment which is easy to apply and up to four times more effective than teak oil. TeakGuard FAQ #2 for Teak Cleaning and Refinishing- MarineStore.com says,
  TeakGuard is a unique water-based polymer which actually sinks into the wood. After soaking into the wood and attaching to the wood fiber, TeakGuard crosslinks with itself and forms a tight bond deep inside the wood. The crosslinking action seals the natural teak oil inside the wood and prevents it from being "cooked" by the sun.
  Despite looking rather poor, rough and weathered teak usually has enough teak oil inside to keep protecting the wood. Rough wood doesn't affect the lifetime of TeakGuard. If you don't mind the rough texture of the wood, then don't worry about it. Just use TeakGuard to keep the mold and mildew away.

BoatUS - BoatTech - Teak Care by Don Casey says,
  Sealers don't feed the wood but, as the name suggests, they seal out moisture and dirt, and seal in natural oils and resins. Unfortunately, the oils and resins may already be lost, so the first step in applying a sealer to old teak is to restore the oil content with a thorough application of teak oil. Clean and bleach the wood to a uniform color, then oil it until it refuses to accept more. Now wait at least two weeks to let the resins dry before you apply the sealer.
  After two weeks, wash the wood and let it dry completely. Sealers need an oil-free surface to attach to, so wipe the wood heavily with a rag soaked in acetone to remove all oil from the surface.

Teak Protector Wood Treatment, Teak Treatment Water Based at Cyan Teak Furniture says,
  Lindsey Teak Protector is a modern treatment for teak that is easy to apply and lasts a long time. The treatment protects your teak and helps teak look great because it helps teak retain the natural warm colour of teak. Teak Protector doesn't let your teak turn black or grey and lasts the entire season. Plus it provides 100% protection from the sun.
  Nearly all teak that is treated with normal teak-oil, turns grey in 4 to 8 weeks. After that, the teak needs to be cleaned and oil reapplied.

Semco Teak Wood Sealer at Jamestown Distributors says,
  Most common teak protectants are solvent and linseed oil based, and oxidize over time. The oxidization of surface oils causes teak wood to appear weathered or gray.
  Semco teak sealer waterproofs and protects teak. This durable protectant maintains a protective coating through winter, eliminating the need for deep cleaning.

Comment at Ipe Deck Finish: 5 Things not to Do : Topcoat Review says,
  I previously used CWF Hardwoods, which is a water based product. I used it on all sides when it was installed new. But I am convinced an oil based product is much better.

Comments at Flooring Forum - GardenWeb:
Always use Oil-Modified Urethane (OMU) to get that deep rich tone. It is important to use an oilbased sealer with colbalt dryers. Tack with lacquer thinner prior to sealing and coat, this will remove some of the oil that hampers the drying. Screen between every coat.
Waterbornes will cure with a dull haze, use two coats of gloss OMU to prevent clouding and top with sheen of customers choice.

Selecting a Finish - Fine Woodworking Article says,
Watco-brand Danish oil, teak oil and a number of other finishes have a mixture of oil and varnish. It's difficult to ascribe accurate protective qualities to these products because manufacturers don't usually disclose the ratio of oil to varnish.

Finishing Teakwood | Teak Finishing

Links:
EXT Wood Protector Finishes
Surface preparation
Teak Cleaning and Refinishing FAQ - MarineStore.com
Mold Mildew and Algae
Cleaning in Painting Preparation & Priming
BoatUS - BoatTech - Teak Care by Don Casey