This a very cursory summary.

Many people are cutting their cable TV service and relying on Netflix and Hulu (see Internet TV).
But what about local channels and news? They are still broadcast over the air (OTA) and you can get them in most cases without installing a big antenna on your roof.

In 2009 the US switched from analog to Digital TV format for broadcast over the air (OTA) TV.
Many people still had old TV's without a digital tuner, so a converter box to convert from digital to analogue was required.
The signals are still brodcast over the same frequencies so your old antenna should work

First let me say that the frequencies didn't change so your old antenna should work.
Channels 2-13 are in the VHF (Very High Frequency) band Channels 2-6 (54-88 MHz), Channels 7-13 (174-216 MHz) with a wave length of 1-5 m
Other channels 14-83 are in the UHF (Ultra High Frequency) band (470-806 MHz) with a wave length of 40-60 cm (16-24 in)
Because of the longer wave length the small flat indoor antennas generally do not work well with channels 2-13.
However some like the Winegard Flatwave FL5500Y is advertised as a VHF/UHF antena.

See Solving VHF DTV Reception Problems | TvTechnology

Test with Winegard FlatWave FL5500Y Amped Indoor HDTV Antenna $80
Our house in Martinsville is 30 miles from NYC.
Almost (some trees in the way) line of sight to the WTC.
New York City Channels:
Station Virtual
Chan.
RF
Channel
Network Mtnsvl
Test *
BB
Test †
WCBSDT 2.1 33 CBS x
WCBSDT 2.2 33 x
WNBCDT 4.1 28 NBC x
WNBCDT2 4.2 28 Ind x
WNBCDT4 4.4 28 NBC
WNYWDT 5.1 44 Fox x
WNYWDT 5.2 44 MyN
WNYWDT 5.3 44 x
WABCDT 7.1 45 ABC x
WABCDT2 7.2 45 Livewell x
WABCDT3 7.3 45 Ind/LAAF x
WWORDT 9.1 38 MyNet/WOR x x
WWORDT 9.2 38 Fox/WOR x x
9.3 Buzzr x x
9.4 Heroes x x
WPIXDT 11.1 33 CW/PIX11 x
WPIXDT2 11.2 33 Ind x
11.3 This TV x
WNETDT 13.1 61 PBS x
WNETDT2 13.2 61 PBS x
WNETDT3 13.3 61 PBS x
* Mohu test from Martinsville - 425' elevation 29-31 mi to NYC.
I got 32 channels. In addition to those above I got
41.1,2,3,4; 51.3,5; 52.1,3,5,8; 58.1,3; 63.1,2,5,6,7,8,9
Channel 9 was marginal until I attached an amplifier. A cheap ($10) only got 58.1, 3 miles away in Warren.
Where I live on the top of the first range of the Watchung Mountains in Martinsville, NJ it is 29 miles to 1 World Trade Center (WTC) and 31 miles to the Empire State Building.
I have a line of sight to the WTC.

† Mohu test from Bound Brook test - 43' elevation - 30-32 mi to NYC
19 channels. Others 41.1,2,3,4; 47.1,2; 52.1,3; 58.1,2.

Notice none are VHS channels (RF channel 2-13).

Most analog stations changed their RF channel in the digital conversion (and most VHF stations moved to UHF) for DTV, but were allowed to keep their old analog channel identification as their DTV or Virtual Channel.
So CBS will stil show up on channel 2 on your TV even though they are broadcasting over RF channel 33 (UHF - 584-590 MHz).
The consequence is you don't need a large VHF antenna like the one you had on your roof and one of the small indoor antennas may work if you are within 25 miles of the transmitter.


At the beginning of 2016 stations starting to move their transmitters from the Empire State building, where they were moved following 9/11 to the WTC.

I got 35 channels with a Mohu. Adding an amplifier didn't make any difference.


Tips:
  • There placing these little indoor HDTV antennas.
  • Bigger is not better.
  • Amplifiers only help if you're far away (more than 20 miles) from the transmitter.
High Gain Antennas:
Antennas are either passive (connected directly to the TV) or amplified.
Amplifiers only help if you're far away (more than 20 miles) from the transmitter.

Don't be fooled by claims of astoundingly high gain. Some manufacturers are marketing small indoor antennas and labeling the boxes with gain numbers between 30 and 55 dB. This kind of unit is actually an antenna paired with an amplifier, and the gain value stated on the package is really the gain of the amplifier and not that of the antenna. While it is possible to improve reception by using a well-designed low-noise amplifier, most of the inexpensive antennas designed this way actually have cheap amplifiers and too much gain. That combination generally overloads the amplifier -- and potentially the receiver as well -- causing signal distortion that can degrade or eliminate DTV reception entirely. Most consumers are better off with a well-designed nonamplified unit, also known as a passive antenna. If television reception does require an amplifier, the best choice is a high-quality, low-noise model connected as close as possible to the antenna.
Source: Antennas Direct | Don't Be Sold on High Gain

Reviews/Tests:
The Best Indoor HDTV Antenna | The Wirecutter

Wirecutter assembled a list of indoor antennas based on top recommendations on Amazon, as well as antennas recommended by respected reviewers from sources like Digital Trends, CNET, Tom's Guide, and Consumer Reports.
They ran test at 15-16 miles from Philadelphia and in Broklyn NY.
  They liked the Clearstream Eclipse.
In Consumer Reports tests, performance varied wildly--so much so that we couldn't really rank them in order of performance, as a model that did well for one tester couldn't pick up any TV signals for another.
The Mohu Leaf and Winegard Flatwave are both popular small flat antenas.
In HDTVexpert's tests 25 miles from the transmitter the Leaf was best. (I think the Flatwave was the un-amplified version.)
At Solid Signal Blog they say "So far, I don't see where one has an advantage over the other."
In Popular Mechanic's tests of amplified versions of both in New York City, the Flatwave got 48 channels, the Leaf got 35 .
Useful Gadgets: Wall-Mounted Indoor DTV Antennas | HDTVexpert
Best TV Antenna 2016 - Indoor HDTV Antenna Reviews | TomsGuide

Others:
HD Stacker TV Antenna and a Channel Master Titan 2 High Gain Preamp. Links:
Internet TV
AntennaWeb Find distance to local transmitters
Amazon.com: TV & Radio Antennas
HDTV
10 things you need to know about Digital TV Antennas
Digital HDTV Converter Box Tests and Ratings
New York City Free HDTV Channels and Antennas.
Television Frequency Table
Best indoor antennas for free HDTV (YouTube) | Digital Trends

last updated 5 Feb 2016