If you assign each person in the world to one of two lists ("Dull People" and "Interesting People"), and rank them by dullness or interestingness, you have to come up with the World's Dullest Person. This makes them interesting, though, so someone else gets moved into the World's Dullest Person slot...
This is a variation by Martin Gardner on Edwin Bechenbach's "proof" that every positive integer is "interesting".

A Blather of Paradoxes