The Intrepid Dr. Girlfriend and I have thus far built robots capable of frightening her dog. We are therefore shamed by this guy (you’ll probably have to scroll down), who has created a Rubik’s Cube solving machine using the Mindstorms kit.
It should be noted that it amounts to a computer controlled system, as a PC program creates the code based on the scrambled state of the cube, but it’s pretty damned impressive nevertheless.
(Thanks, Cory!)