A simple spinning toy or the swing thing made in Lego, inspired after seeing this video
http://www.youtube.com/watch?v=J-OY0KxRdgQ

This one features Qui-Gon Jinn and Darth Maul spinning around a 4 pole design
Its very simple and easy to build. With the right rubberband, it can run for a long time. This particular one tested to over 15minutes

Basically you have a central tower which houses the rubberband and four poles around it to for the wrapping and unwrapping.
This is a very simple and straightforward project which I believe can be easily built just by looking at it

Step 1: Swinging Arm and Winding

The swinging arms should have a smaller diameter than the distance between two opposite poles, the arms should also be below the tip of the poles.

To wind it up you simple slide the link away and remove the arms and wind up the rubberband.
You can try a different number of arms and different number of poles it works well with just one arm, 2,3,4 is still ok but i have not tried beyond that. Two arms and four poles is my favorite configuration.