One of the best uses for the Raspberry Pi is to teach kids (and adults) basic programming skills. AppGameKit's a bit of free software that does just that.
The software isn't exactly the simplest game creation software out there, but it does pack in some useful stuff for the Pi specifically, like access to the GPIO pins so you can code in physical inputs/outputs. Plus, anything you make can be deployed to just about every platform out there, including the Raspberry Pi itself.
If you're looking to mess around with making games on the Pi, AppGameKit seems like a step up from the built-in Scratch software, but still manages to be simple enough for beginners.