An extensive list is at MSE, including pointers to dedicated web sites, such as this one.

I might add

The Stanford Mathematics Problem Book 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.

An extensive list is at MSE, including pointers to dedicated web sites, such as this one. A particularly comprehensive collection is in Problems and Solutions in Mathematics, with a list of advanced topics (including Galois theory, homotopy/homology, differential geometry of manifolds, measurability and measure, PDE's).

I might add

The Stanford Mathematics Problem Book 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.

The Stanford Mathematics Problem Book 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.

An extensive list is at MSE, including pointers to dedicated web sites, such as this one.

I might add

The Stanford Mathematics Problem Book 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.