Here's a couple of well-known simple topology tricks:
Tie ends of a long enough piece of rope to your wrists, while wearing a loosely fitting jacket or sweatshirt. With your arms tied like that, take the jacket off your back and put it back on inside out. It's easier to figure out how to do it than to explain it in words, so I'll skip the explanation. The more risque version is to tie the ankles and do the trick with pants.
The other one I haven't tried, but maybe it can be done at a party if you have a stick and some plasticine around.