The main reasons are:
1) Even illumination of the entire screen.
Full array LED backlit LCDs can have nice, even illumination as well, but traditional CCFL backlit LCDs and the edge-lit LCDs all suffer from uneven illumination that often includes corners or edges that are brighter than the rest of the screen, "clouding" in the backlight, or just plain uneven lighting behind parts of the screen.
Furthermore, even the best full-array, local-dimming LED backlit LCDs suffer from "blooming", which looks like a "halo" of light around small bright objects that are on a dark background.
2) Deeper black levels.
Again, the best full-array, local-dimming LED backlit LCDs can deliver excellent black levels as well (aside from the "blooming). But the rest of the LCDs and edge-lit LED LCDs still can't match the deep black levels of the best plasmas.
3) Off angle viewing.
You can pretty much look at a good plasma across its entire 180 degree front area and the colors and brightness will not change. On LCDs - regardless of the backlighting technology - as you move off angle from dead center, the colors will shift and the far side of the screen will start to wash out and look brighter than the near side of the screen.
4) Motion.
LCDs still exhibit some blur and motion artifacts.
5) Smoothing/120Hz effect/Soap opera effect.
While you can always turn this stupid processing off on LCDs, many people don't. Plus, if you do turn it off, you often lose the dejudder processing or increase the motion blur. Some plasmas offer a "smoothing" mode as well that makes 24fps content look like it was shot on a camcorder, but you typically have to go into the menu and turn it ON, rather than how most LCDs make you search through the menu to turn it OFF.
6) 3D
Plain and simple, 3D on LCDs looks like *** because of the cross-talk that is a result of LCD panels not being able to refresh fast enough to avoid it (same reason LCDs have motion blur). The best plasmas deliver the best 3D experience - and that includes 3D in a movie theater.
7) Price to performance ratio
At 50" and above, plasmas still tend to offer better picture quality in all of the areas above for the price. The price gap is closing on these larger screen sizes, but the LCDs that are cheaper are markedly worse in picture quality, so plasma still holds an edge here.