LCD vs Plasma

Advantages

LCDs are good for still images and make good computer monitors. So, if you're looking for a screen for TV and computer use.
Quality LCDs have excellent brightness level pictures.
LCD flat panels don't take up room and can be mounted on walls.
Quality LCDs have a fairly long life, especially compared to older models.
There are more 1080p LCD models than plasma (you'll see a sharper picture with a 1080p model).

Disadvantages

LCDs are not good for fast-moving pictures. When an object moves quickly across the screen, the image "delays" (there are trails of pixilation or blockingess), because the screen can't keep up. For this reason, LCDs that are 37" or smaller generally have better image quality because the delay is less noticeable than on larger LCDs.
LCD TVs have difficulty with black levels
LCD image looks great when you're staring directly at it, but if you are watching from a slanted view the quality of the image can diminish greatly.
LCDs are very expensive over 35"
LCDs sometimes have pixel failure. This isn't a common problem with top name brands, where one or two pixels might eventually die, leaving a black dot here and there. This is hardly noticeable unless you're standing directly in front of the screen (considering a 20" LCD screen has 30,000 pixels). However, in cheaper models where 10% of the pixels could go out, the TV may become unwatchable.

Advantages

Top name brand plasmas have a fairly long life, lasting about 20 years at a six hours per day pace.
A plasma screen has a field vision of about 180 degrees without loss of picture quality. That means you can watch the screen from any angle.
Plasmas are very bright (about 4-5 times brighter than the average TV)
They have great contrast ratios (enables them to show better shadow detail)
They have excellent picture response. There is virtually no delay (blockiness or pixilation) like with LCDs.

Disadvantages

Plasmas can have burn in problems. Plasmas do not make as good computer monitors as LCDs. If you were to leave the Plasma TV on for 24 hours a day and there was an image that remained constant on the screen (like a logo), you would run the risk of that image permanently burning into the screen. However, the chance of this happening is often over-exaggerated.
Plasmas are not available below 37 inches.