Here's a neat little case I picked up for my iPod. Manufactured by Griffin, the Reflect case does just that. When your iPod is off or the backlight is off the screen disappears behind the mirrored chrome finish. Turn on the iPod and it magically appears. I also like the fact that the bottom of the case (where the cable connector is) is completely unencumbered so you can plug the cable in, or attach it to a speaker set, without having to take the iPod of the case.
In any regard, here's a short little video of the case in action. Even got a bit of Jason Calacanis doing one of his video podcasts in this to show how the video appears through the case. (He needs on camera lessons. I'm available, Jason.)