It used to be a problem with plasma, but the newer sets don't suffer from it.
Do the latest Plasma TVs suffer screen burn-in?
No, Plasma TVs, made in the last couple of years, adopt two techniques to handle this problem.
The new motion adaptive anti burn in technology makes the ghosting effects undetectable by TV viewer. It is found that the use of green phosphor increases the overall life of phosphors.
http://www.plasmatvreviews.org.uk/articles/new -facts-on-screen-burn-in/