Tape vs Dope
I thought teflon (PTFE) plumbers tape had replaced pipe dope, but recently found out there are situations for both.
One general solution that I've seen recommended a lot is to use both. Both dope on top of tape and tape on top of dope.

However at "Trouble with Teflon. Use Pipe Joint Conpound?" - Plumbing Forum - GardenWeb they say,
"DO NOT use both PTFE & dope on a joint, either or is fine but never both."

Some gray paste dope is oil based and should not be used on plastic pipe.
At "When should pipe dope vs thread tape be used?" - Home Improvement Stack Exchange they say it depends on the type of threads.
Fuel threads (NPTF) create a mechanical seal so don't need sealant.

At the same forum lazypup says,
Personally I always use dope on all joints that are intended to be a permanent part of the water or gas distribution systems, especially if the joint will end up in a concealed or difficult to reach location.
On the other hand, dope can be a bit messy to work with so I use PTFE on all final trim out NPT pipe thread joints such as when attaching a shower head to the shower arm or other semi-permanent joints that will often be changed.

Sealant for pipe type:

• Metallic pressurized water fittings: dope because it will lubricate more effectively without being damaged by hard threads and you're at less danger of breaking the fitting due to over tightening.
  NPT - National Pipe Thread Tapered has a taper, which often allows a seal to be made without a sealing agent. But this type of thread when mated, may contain slight gaps between the major and minor diameter of the threads. Because of this, a thread seal agent may be required.
• Plastic pressurized water: tape because it will slide equally effectively against plastics, and will not "over lubricate" lending to breaking the fittings. Also, certain dopes can react with certain plastics (though most are probably safe).
  However at shut off valve leak - DoItYourself.com Community Forums, lawrosa says,
  "My experience with plastic threads and Teflon tape is that it ALWAYS leaks. Use a semi-liquid thread sealing compound (such as Teflon paste) compatible with plastic and it will seal."
• Metal/Plastic drains: dope because it will more readily fill gaps to "seal" if there is no pressure backing it.
• Air/Gas: tape (or specialized dope, or nothing at all, depending on the fitting) because you don't want to potentially spread oils or other dope through your appliances/tools.
• Compression fittings don't need sealant, but some use them for lubrication. Oil will also work.

At Pipe Dope On Teflon Tape? - Terry Love Plumbing & Remodel DIY & Professiona Forum, Terry says,
"Places I don't use tape or paste? - Compression fittings (at most something like silicone spray or WD40 works well)
- Plastic p-traps
- Water heating connections when using flexes with rubber seals.
- Flex connectors for lavs"
The above items don't need paste or tape.

Petroleum-based pipe dope is not intended for use on threaded PVC, CPVC or ABS pipe and fittings since it will deteriorate the plastic.

There are several types:
TFE - Teflon - white
Professionals may use one of the following because they have wider application e.g. gas lines.
RectorSeal chemical specialty sealants and other related products designed for professional tradesmen Pipe Thread Sealant Chart" Gray
Hercules Pro-Dope - Oil-based thread sealant. Not for use on plastic pipe or fittings.
Megaloc

Tape comes in different thicknesses. white - single, yellow - double, pink - triple.
See: Teflon Tape Vs. Pipe Dope - www.WaterHeaterExplosions.com -

Links:
Practical Q's on Plumber's Putty, Dope, Tape - Straight Dope Message Board

Terms:

Pipe Dope - Thread Sealant Paste to seal pipe joints
PTFE - Teflon (polytetrafluoroethylene)
Plumbers Putty - A clay-like substance used to seal areas of a sink that may be exposed to water
   but will have no water pressure applied to them.
   Most frequently used to seal the upper portion of a drain - called a 'basket drain' - to the sink. 
Plumbers tape - PTFE tape used to seal around threads.
See plumbing for others