Plasma falls victim to the image burn problem on screens that have station logos placed in the viewing area that never change, like CNN for example, or MSNBC, or any other station that uses a logo on the screen at all times during a program. LCD doesn't have that problem.
I heard about that, but I understand some makers are now compensating for that by having a image that floats in a very small, imperceptible way but enough to prevent image burn. I am sure that the next generation will all have that image burn problem solved.
Most newer plasmas use reformulated phosphors that are less prone to burn-in. Newer sets also subtly adjust the picture position to further reduce risk of burn-in.