For Christmas, I gave my 8-year old an origami kit called Story-gami by Michael LaFosse and Richard Alexander. This has been an absolute hit and I thought I'd share it with you. Included in the kit are origami (Japanese folding) paper, a book and a DVD with great little story adventures that result in a beautiful origami work.
My 5-year old has been able to do these as well: each day I'm in charge of pausing the video while my two kids go through the demonstrated fold which comes as part of the story. We love this kit; the nice, kid-friendly storytelling approach to creating something quite intricate out of a mere square of paper is excellently done.