I work in TV post production and broadcast. I'd love to weigh in here!
GENERALLY speaking - plasma is considered the best display technology (PQ-wise) of the three mentioned here (really there are two technologies mentioned, as LED is a subset of LCD TVs) - and by that I mean a (good) plasma TV will most closely rival a CRT (tube) TV in terms of black levels and processing delay.
CRTs, being analog, have no processing delay. All digital display technologies else do, and it's one of the dirty little secrets of current TV technology. A high end plasma (say a Panasonic Viera or a Pioneer Kuro, if you can find one) will, on average, have less processing delay than LCDs. That means the video has a better chance of being synced to the audio. For certain sources like Blu-ray, the HDMI handshake will sometimes (but not always) help with the processing delay, but other sources like set top boxes (cable, satellite TV, etc.) won't always have that luxury. Watch broadcast television closely, and even on a CRT you'll often see that the picture is not perfectly in sync with the audio - and the video processing delay in digital TVs can only compound the problem - consider processing delay when purchasing a TV.
Next is black level, and this is another area where (again, GENERALLY speaking) plasmas come out on top. LCDs, because they MUST be backlit (either by CCFL or LED), will not produce the absolute black that you get from a CRT. Plasmas do a better job here because they do not use a backlighting technology. Sometimes you see insane, unrealistic contrast ratios (5,000,000:1) because newer LCDs will selectively turn on/off certain portions of a screen's backlight, but that is an artificial number and should not be used to indicate real world contrast ratio. When you see numbers like that, you can be certain that it was a sales team that came up with it, not an engineer.
You'll also find that, because plasmas do not rely on a backlight to create contrast, their acceptable viewing angles are generally wider, so there's more of a sweet spot when viewing.
Plasmas are far from perfect, though, and have several disadvantages when compared to LCDs - they cannot currently be manufactured as thin/light as their LCD counterparts. They are also generally less green, consuming more energy and generating more heat than LCDs. Also, if you are looking for a giant screen, LCDs are available in larger sizes than plasma panels. Similarly, nobody manufactures a small plasma panel because it's too expensive - but I am going to assume we're talking about a nice big screen here!
Finally in LCDs corner, they can display a brighter picture (some might call it artificially bright) than plasma panels. Because of this, a room that receives a lot of direct sunlight might benefit from LCD. HOWEVER, a very good rule of thumb would be this: If you currently have a CRT in a room and it is bright enough for comfortable viewing, a plasma TV will absolutely be bright enough. The one room in my house where there is a TV is the great room, and the (CRT) TV is against a wall which has two windows, a sliding glass door off to the right side, an entry way into a bright living room to the left, a window in the back AND two skylights - and the CRT is plenty bright in all situations - so I know a decent plasma will be as well.
If I were purchasing today, I would not consider LCD for my viewing pleasure. I have seen both technologies up close in controlled environments, having received private viewing demos from some of the usual suspects, and I know where I'd put my money.
In my opinion, LCDs are good, plasmas are better. Oh, if they hadn't abandoned SED TV, a technology that knocked my socks off!!!
Just one quick note about stores. Most stores are the worst place to evaluate a display. Competing with fluorescent lighting and other TVs, you'll generally notice that all the controls you'd generally want to turn DOWN in your home (like contrast, saturation, sharpness) are turned up to their maximum values. High end AV showrooms will often have dark viewing areas, and the TVs will be calibrated. These are few and far between though, and it's just a shame that people have to evaluate TVs in such hostile environments!
OK - reading back it's long-winded, but I think you all know where I stand!
