Not practical, but awfully cool: Austria-based Klemens Torggler is on a mission to re-invent the door, by breaking it into two sections and adding hinges that move in a different axis than you'd expect. Observe:
That one's called the Evolution Door and it's skinned in fabric; it's difficult to tell from the perspective in the video, but it appears the corners swing out towards the user in 3D space while in motion, then return to their original plane when open or closed.
A more basic, easier-to-comprehend version is Torggler's steel Stahltür model, whose motion is limited to X and Y axes:
Finally there's Torggler's latest version, which is made out of glass and requires a more complicated hinge. This video clip comes with a bizarre 10-second animation at the front that I cannot explain:
Torggler's website is light on describing intended applications, and this design would never fly in America without safety modifications because we love to sue people, but it's an intriguing mechanical feat nonetheless.