LCDs - They are cheaper than LEDs and offer average to good picture quality, depending on the make and model.
LEDs - Expensive for really great units, and the true motion or motion smoothing can be a problem to some people. The LEDs you see in shops that look surreal, as if the motion is kind of TOO crisp, probably using a built in feature to smooth out frames to up the FPS. This causes movies to look weird on some sets but some games look better with it. All down to taste on this one.
Plasma - Has the best black levels, most gamers swear by them. They are heavy and power hungry, burn in can still be an issue if you forget to change channel for a week or play the same game for a few days. Most newer plasma sets have built in pixel shifting so burn in is less of an issue. Always read the user manual with a plasma screen, every manufacturer has their own way of approaching the burn in issue. They are cheaper than LEDs as well.

