Some of the older Plasma screens had problems with "burn-in" from video games and leaving DVDs paused for too long, but that's not the case for LCD screens. See:
LCD Image Persistence
LCD screens are not completely immune from burn-in, and even if they do get a burn-in image, it's most likely not permanent. I've done quite a bit of research on this, and have seen only a few posts around the internet in the past 5 years for LCD screen burn-in or ghosting (partial image stuck on a screen). Newer technology TVs have overcome most of these problems, including most of the new Plasmas.