LCDs are generally brighter and can cope with ambient light more easily because they tend to have non-reflective viewing surfaces. If you'll be doing most of your viewing in the daytime or in a brightly lit room, LCDs are a good option. Also, if Blu-ray or HD-DVD are on your list, it's pretty easy to find 1080p LCDs these days. Newer LCDs have backlights with a wider color spectrum, so they're capable of rendering more accurate colors than the traditional LCD cartoony look.
Plasmas have lower black levels and can achieve significantly higher contrast ratios than LCDs. You get better shadow detail and a deeper, more involving picture. You need a darker viewing environment to really appreciate this benefit. 1080p plasmas are extremely expensive (not sure what others are available aside from the Panasonic 65", which is outrageously expensive). Pixel structure on plasma is more evident than on LCDs, so you'll want to sit a bit further away.
Unless you require a really bright display or you can't do without 1080p capability, I'd go for the plasma. Consider Panasonic, Hitachi, and Fujitsu.
If you go for LCD, take a serious look at Sony's XBR series. Probably the best LCDs on the market today.