Some basics as I understand it:
Plasma
Brightest image (if you have a bright room), most vivid colors, but can exhibit streaking, ghost images, and slow refreshes. These are also the most expensive (except for the big LCDs) and have the shortest lifespan. They are the preferred choice of the Corporate customer, for signage and advertising, and quick depreciation schedules
LCD
These are great small (like many flatscreens) but can get really expensive when you start getting to 50 and 60 inch screens. They are also pixelated by design so they do not have the highest resolution image.
DLP
IMO the best bang for the buck. I guess these arent really flatscreens, but they're narrow enough. Good lifespan (extendable with an albeit expensive bulb replacement)
Good article:
http://www.dlptvreview.com/dlptv/plasmatelevision.html