The first place to look is the problem instance collection of INFORMS, the Institute for Operations Research and the Management Sciences. They have links to all sorts of interesting problems like graph coloring, traveling salesman and combinatorial auctions.
For factoring, you can make some real money by solving the RSA Factoring Challenges.
For graph isomorphism, check out The Graph Database. The graph database only seems to have isomorphic graphs but a good isomorphism tester should give the isomorphism. I haven't been able to find a collection of nonisomorphic graphs that fool many isomorphism testing algorithms. See also the Nauty algorithm.
For satisfiability, there are algorithms that seem to generate hard instances. You can also take problems like graph coloring from the INFORMS site and convert them to satisfiability questions.