Sam Loyd invented this enormously popular puzzle in 1898, and it's one of my favourites. You'll have to excuse the stereotyped artwork, though.
The puzzle shows some warriors around a globe. The inside circle is a separate piece of paper, attached at the center so that it can turn freely.
Behold the globe with 13 warriors.
But give the globe a turn...
and one warrior disappears.
What's happening here? How does the thirteenth warrior disappear? And don't say the Rapture.
If you want to print it out and try it yourself, you may want to use the very nice PDF available on this page.