Each has their own advantages and disadvantages. Overall, LCD will meet the needs of most people over plasma, and cost less in the long run. But, the plasma technology advantages may have an overriding appeal to some people.
Plasma PROS: Better contrast ratio, better ability to render deep blacks, more color depth, better motion tracking (response time), and more availability in very large screen sizes.
Plasma CONS: more susceptible to burn-in (although this is not as much of a factor now, due to technology improvements, such as "pixel orbiting"), more heat generation (as well as more power consumption, like 2-3 times that of LCD), does not perform as well at higher altitudes, naturally darker image and screen glare in brightly lit rooms, heavier weight, more delicate to ship, and harder to find in sizes less than 42".
LED/LCD PROS: no burn-in susceptibility, cooler running temperature, less screen glare, more functional at high altitudes, longer display life (although improvements are being made in Plasma screen life), looks better in brightly lit rooms due to the ability to produce a naturally brighter image, and less power consumption than Plasma.
LED/LCD CONS: Lower contrast ratio, not as good rendering deep blacks, has a narrower side-to-side viewing angle, and not as good at tracking motion (although this is improving, especially with the implementation of 120Hz refresh rates (and some now offer 240Hz on higher-end models). LED units will generally cost a little more than LCD and plasma, but the power savings over plasma will eventually render the difference moot.
Ultimately, the best thing to do is visit a store and witness the same movie being played on a variety of screens. This will help significantly in making a decision.
Personally, I don't like the fact that Plasma TV's are much heavier and more fragile, which presents a problem when moving or changing a room layout. Plus, their power consumption is quite a bit more (2-3 times that of LCD), as well as generating a lot of heat. LED/LCD is a more "green" technology.
Some links:
Difference between LCD, LED and Plasma TV's
Should I buy LCD or Plasma? (About.com).
TV power consumption chart