Yoyo Games' Game Maker is a pretty common tool.
If we're talking bright, BRIGHT kids, who have an attention span and would be committed to learning something, you may also want to try Python. This one is definitely a good games-oriented HTML book for Python.
Chances are, Game Maker will be much better suited: You can get an obvious end product.
I also haven't used it or heard about it, but Ruby for Kids - Make Games in Minutes! looks promising.
(I think I may not be a good example, but I started off with Flash aged 11. :P)