I have been running into this question a lot from several different people and places (television forums, friends, family, news sites) so I wanted to help and clarify.

You WILL NOT need to buy a converter box if your TV is currently built with a digital converter already inside. You can know this first by when you bought the TV. The law is that after March 1, 2007, all TV receivers shipped or imported into the United States had to contain a digital tuner.

Also, effective back on May 25, 2007, it was required that anyone selling a TV without equipment that does not include a digital tuner to disclose right away that the TV only has an analog tuner. So...  buying a digital to analog converter box to receive broadcast television after the transition date will be necessary if do not currently subscribe to some form of paid for TV service.

I just bought a TV: will it work?

If you bought your TV within the last few years, it's good to know that any retailer must have this posted on or near a TV that may only be analog:
 
This television receiver has only an analog broadcast tuner and will require a converter box after February 17, 2009, to receive over-the-air broadcasts with an antenna because of the Nationʼs transition to digital broadcasting. Analog-only TVs should continue to work as before with cable and satellite TV services, gaming consoles, VCRs, DVD players, and similar products. For more information, call the Federal Communications Commission at 1-888-225-5322 (TTY: 1-888-835-5322) or visit the Commissionʼs digital television website at: www.dtv.gov.