LCD flat panel and microdisplay RPTVs (DLP, LCoS) have no risk of burn-in. Plasma and CRT rear projection only have moderate risk. I used a CRT rear projection for video games for about 6 years, and I had no problems at all. I'm currently using a 50" plasma for video games, and again I have had no problems. Unless you leave a static image on the screen for 10+ hours, it really shouldn't be an issue.
I am moving out of my house into the "real world" with some friends of mine. I am looking to buy a new TV. We play videogames alot and I wanted to know which TV types (plasma, LCD, projection) etc were safest when it comes to long hours of videogames. Also, will having the screen bright ruin the screens of these types of tvs like I have heard?