I love this Möbius Gear design, made by Aaron Hoover for a Procedural Solid Modeling class back in 2009. It looks impossible at first glance, but the trick is that the inside gear is actually made from a flexible material, so it can deform as it spins around the fixed outer gear.

There’s also a different gear arrangement referred to as a Möbius Gear, though I think that technically it’s more of a Möbius Gear Train. Has anyone attempted to actually build one?

[Thanks, Xander!]