As I made my way through Portal 2, I came across this amusing sign (click for full-size image):
Think of it this way: Suppose someone gave you a catalogue about catalogues, called SuperMegaCatalogue, that contained every cataglogue that had ever been printed. Would SuperMegaCatalogue be featured in the pages of SuperMegaCatalogue?
As the Wikipedia page puts it:
Let R be the set of all sets that are not members of themselves. If R qualifies as a member of itself, it would contradict its own definition as a set containing all sets that are not members of themselves. On the other hand, if such a set is not a member of itself, it would qualify as a member of itself by the same definition.
Or, to use the terms of symbolic logic: