Inspired by http://www.thingiverse.com/thing:4244 this is a box that opens when you twist the outer rings in opposite directions. See this video by Labmat: http://www.flickr.com/photos/matthewlaberge/5101233486/

Edit I: Design has been modified to increase the clearance between moving parts. I've also centered and oriented the parts in better positions for printing.

Edit II: Design files posted. DXF, STEP and the original CATpart for those with access to Catia. Thanks to everyone for your photos, videos and design feedback!

Edit III: Be sure to check out Jon Hodgins' version: http://www.thingiverse.com/thing:5589

Print 5 shutters and one of everything else. Assemble with filament or M3 screws. You will probably need to sand some surfaces and drill out some of the holes. Still offering bonus points for a video of it working.