Some thoughts:
A game of speed like one of those toys that has blinking buttons... you have to click the button while it is blinking to score points. If you want to start simple you could just change the icon picture of the button or change the text of the button in place of the blinking.
Quiz show? Connect 4? A create your own adventure game like those create your own story books?
You could be creative with simple existing games and make your own rules. ;-)
