On CRTs, images being burned into your screen rarely ever happens. One thing that does suck about CRTs, though, is that if you have any stereo speakers nearby, make sure they have magnetic shielding, because otherwise its going to leave big discoloration which you have to get rid of by either turning the TV on and off constantly, or if that doesn't work, manually degaussing it.
On plasma TVs, however, are far more susceptible to burn-in than CRTs, from what I've read.
I'd stick with LCD. It's cheaper than plasma, and honestly, you can't really tell the difference.