CRTs are those old-school monitors everyone has. Big, bulky, heavy, ugly, and (sometimes) noisy, they are the low-end monitor option for your typical gamer. However, a decent CRT monitor has an small advantage over LCDs in the fact that they are like color TVs, and can display more colors than a (cheap) LCD. Plus, they have a higher theoretical refresh rate than (cheap) LCDs. Overall, these are the best choices for anyone looking for a budget PC with a good display.
LCDs are like CRTs cooler, slimmer, stylish older brother. Instead of being like little desk-hogging monoliths, they take up very little desk space, and generally look good. The disadvantage of this is that cheap LCDs tend to... well... suck, especially when it comes to colors and refresh rate. However, an good, well-priced LCD can be found that trumps CRT in every way, so the typical "Gamers don't buy LCD" theory is shot. Also, as an advantage, LCDs have whats known as "Perfect Screen Geometry", allowing you to see perfect shapes and pixels, instead of all resolutions blurring or stretching them.
Plasma is like LCD's older, more expensive, more anal, show-offy asshole-like brother. If you've ever seen an LCD TV, you know they rock the boat- at a starting price of around $1000. When for $1000 you could upgrade your computer to a meggido pimp machine, I don't see the advantage of these. The only time I've ever heard of them being used effectively is by rich people in living rooms as like a media center/gaming center. And even then, that's a little too expensive for my tastes.
So, which is best for a gamer? Lets take some situations for example. Say there are three people:
Joe- He's a hardcore l33t gamer who plays CS and UT, and does basically nothing else. He's got $500 for a screen.
Fred- He's a hardcore... web programmer who does the occasional graphic design job. He's got $400 for a screen.
Steve- Hardcore downloader who constantly downloads and watches the latest... legal... shows. He's got $1000 for the best screen he can get.
Okay, first, lets look at Joe. Joe obviously needs a high refresh rate and a big screen. Screen geometry, color range, and general style aren't going to impress Joe, because Joe is going to play seizure games.
Reccomendation:
Okay, for each reccomendation, I'm going to reccomend a LCD, and then a CRT. Obviously, Joe is on the "High End" with $500 spending money, so obviously lets hook him up with something that really kicks ass.