We're just a little more than a year away from the end to analog TV broadcasts. After February 17, 2009, your old analog TV will no longer be able to pickup analog TV broadcasts, as the government is freeing this bandwidth up for new usage. There are many options for your old TVs, if you're not ready to replace it.
You can apply for a $40 coupon from the government to go towards a digital tuner. Go to the TV Converter Box Program website, ran by the Department of Commerce and the National Telecommunications and Information Administration to find out more -- you have until March 31, 2009, or until coupons run out (the site does not list how many coupons are available).
The TV Converter Box Program website is full of good information (try the FAQs), as well as there are many other sites with good information. You might start with the Dallas Morning News' Tech Writer, Andrew D. Smith and the National Cable & Telecommunications Association.
If you have cable or satellite TV, you should not have any problems continuing the use of your analog TV. You can also use your analog TV for video games, your VCR, and DVD.
To learn more about what the government will do with the freed up analog spectrum, there has been a lot of controversy, and there are plenty of opinions. Computer World published a good article at the end of the year that covered many of the issues, in particular as it applies for the pending auction on Jan 24, 2008.