An extensive list is at <A HREF="https://math.stackexchange.com/questions/306828/list-of-problem-books-in-undergraduate-and-graduate-mathematics">MSE</A>, including pointers to dedicated web sites, such as <A HREF="http://www.mathpropress.com/mathBooks/">this one.</A>

I might add 

<A HREF="https://archive.org/details/TheStanfordMathematicsProblemBook">The Stanford Mathematics Problem Book</A> by George Polya and Jeremy Kilpatrick.

> These 20 sets of intriguing problems test originality and insight
> rather than routine competence. They involve theorizing and verifying
> mathematical facts; examining the results of general statements;
> discovering that highly plausible conjectures can be incorrect;
> solving sequences of subproblems to reveal theory construction; and
> recognizing "red herrings," in which obvious relationships among the
> data prove irrelevant to solutions.