I thought that a screensaver was pointless on a LCD panel until I left my old laptop running for a weekend while I went out of town. When i came home, the screen had never powered off and when i closed the browser that was open, there was a shadow of the title bar and the X in the top right corner. I thought that the screen was permanantly ruined, but honestly after about a week, it had faded away.
Since then, I make sure to set a screensaver and power off time. Especially on my desktop, since you can't turn my monitor off with a power button.