Origami involves spatial thinking along all stages. Imagine being the one generating the original set of instructions for a design.
MIT has a whole paper folding club (?). Paper folders make good engineers.
Origami can also involve curves, and some people choose origami as their livelihood. (links from GreatMap).
Origami – one spatial way to make your brain work well. Here is a list of other spatial activities, and not only for children.
diana maps 
Diana,
What a great blog. I think these origami is wonderful tool for helping adults understand spatial thinking.
CAF