Plasma has burn-in, so if you watch the news for hours, and change to something else, you'll see a ghost image from watching the news. Had that happen at a house I went to today. Turned the TV on for a couple minutes, switched inputs, but there was a completely black screen up and no signal. You could see the outline of "CNBC Alerts" Nasdaq, Dow, and the like. Also, if you're at a very high altitude, like the mountains here, where Bill Gates has a house up in the Yellowstone Club, there are possibilities of your television messing up due to the lack of air pressure. The screen has pink flashes in various areas.
Plasma has two pieces of glass with the substance between the two, and little pockets where the plasma is electrified. The glass is presurized so there isn't too much or too little space between the two.
LCD TVs are little lights and shutters for each pixel. If you have a flat panel computer monitor, that's what it is.
DLP, rear projection, is just a projector displaying on the inside of a TV. The only thing that can happen to these is problems with electronics or the bulb going out. Bulbs can be replaced. Have a problem with a dead pixel on your LCD, and you're stuck with it. Have something happen to your plasma, you're stuck with it. Have a bulb on your DLP go out, you replace the bulb for a couple hundred. They're also usually less expensive.
Go to a GOOD television store like where I work. One that has around 50 TVs of varying quality, and pick one in the price range you're looking for. Samsung is our best seller. Wal-Mart has cheaper TVs, because the quality is poorer. Same name, different model number. Just check it out.
Crutchfield is a good website to do comparisons for features and cost. But if you want to know picture quality, just go and play with the TV you want.
It also depends on where you have your TV for what you get. DLP isn't the best for a bright room. Plasma can have a glare from the glass. LCD has the same type of finish as DLP, which is like an eggshell. It's smooth, but not glossy like plasma. Also, the closer you are to the TV, the smaller you want. My uncle has a 42" Toshiba REGZA, and sitting 10' away, the picture is great. Smaller wouldn't be as nice, and bigger is just overdoing it.
Where you have it located as far as sitting down is important on what you choose. If you want to mount it to the wall, don't get DLP. A DLP is like a thinner, lighter version of a tube TV.
Don't forget what you're hooking up to your TV. If you get an HD TV, you want HD picture. You're going to want HDMI or at least component video running to it (RGB "picture" + W/R "audio"). HDMI can pass 1080p for your best picture and sound on one cable. Standard definition will look horrible, and you won't be able to stand it. What you could stand on your old TV, you won't be able to on your new. So don't forget to get an HD cable box or satellite receiver/dish.