Echochrome seems pretty cool. It is a puzzle game, with game play involving rotating a world occupied by Oscar Reutersvärd’s impossible constructions to be traversed by a mannequin figure. I don’t know who Oscar Reutersvärd is, but he sounds like an awesome guy.
I also learned that in the Star Trek: The Next Generation episode “I, Borg”, a plan was made to destroy the entire race of Borg—malevolent cybernetic aliens whose minds were interconnected—by showing one of the Borg a picture of a highly complex impossible constructions. This plan was dismissed as being genocide, so its potential results were never seen.
Wikipedia is awesome.