The same places that recycle computer monitors in your area likely recycle televisions, too, because their technology is quite similar. If you can't find a charity or friend who needs your old television, drop it off at your nearest electronics recycling center.
You may have heard about the switch from analog to digital broadcast television; essentially, after February 17, 2009, all full-power television stations will have switched from analog signals to digital. The switch will affect you only if you have a television that's not hooked up to cable or satellite television services. If you have a television that receives free signals over the air with an antenna, you'll still be able to use your set, but you'll need to add a digital-to-analog converter box for $50 to $70.