I've owned a Samsung plasma for about 4 years now. I will see residual images on the screen from a static image, such as tickers or station logos, or when I am gaming. I will sometimes see the image if I turn the TV off and back on hours later, but it is never permanent. Static images are a normal part of programming where I live.
I recommend reading this CNet article regarding "burn-in" to help put your mind at ease.
I have just purchased a second large screen TV, and this time opted for a plasma due to rave reviews by cNet and other authorities. It may have been a mistake, not because there's anything wrong with the TV. The picture is, as the cNet reviewer said, "jaw-dropping." I find that I am paranoid about burn in to the point I am not enjoying the device. When a bar or network logo stays on the screen for more than a minute or two I'm screaming "Get it off! Get it off!' Then I change the channel. The other three TVs in the home are LCD so this was never a problem before. Are there any Lucy Van Pelt wannabees out there who will step into their 5-cent psychiatric help stands and provide some much-needed therapy?