My brother-in-law, Alec, got me a GREAT book for Christmas called Magic Books and Paper Toys.
It is AWESOME! There are some very creative and innovative little paper items, along with some classic ideas, like cootie catchers. I very much recommend it if you are looking for some interesting ideas to try.
One toy that they feature is what they call a flexagon. This is a paper toy that you unfold. And unfold. And unfold. You can continue to unfold it forever, which seems impossible and is terribly hard to describe, so please look over these photos of a flexagon that I created for my brother-in-law as a thank you for the nice gift.
For another kind of flexagon from the same book, check out this recent post from a fellow blogger (and new-found paper buddy): http://extremecards.blogspot.com/2009/01/flexigon.html