Hardy and Williams have "The Red Book of Mathematical Problems" and "The Green Book of Mathematical Problems", with some good analysis, series, conbinatorics, and group theory.
de Souza and Silva have the more advanced "Berkeley Problems in Mathematics".
And finally, another one I leaned on in studying for the Putnam was Dixon's "Problems in Group Theory".
Although I do really like Polya and other's books on problem solving, I always found that I got more from them the more I actually worked through real problems. Others have mentioned actual problem books from the Olympiads and Putnam, which are of course great resources here as well.