Just about every form of compactification. The compactification of a compact space is itself, and a compactification had better be compact or it shouldn't be called a compactification.
The same thing goes for completion of metric spaces, of course. (I know, shouldn't post two answers in one for this kind of list, but they're closely related and trivially known for everybody. I put them here for completeness' sake (no pun intended).)