You know, one of these days when I'm bored, I'm going to make a gigantic list of every single function space (vector spaces of functions) I've ever heard of. Considering the fact that I've seen a lot of 'regularity spaces' (in a miserably failed attempt to come up with a new Sobolev type compactness imbedding), a lot functions spaces that arise in a more banach space theory setting (for my Lp compactness research, though I couldn't even understand the definition of most of these spaces at the time, and probably still can't hah), and now a lot of Banach spaces of Analytic functions via my studying operator theory now (I guess I wouldn't count noncommutative functions spaces since they really aren't function spaces).

I find it hilarious just to think of how many dozens of dozens of spaces I can come up with. God I love analysis :).