Often, I find that the good problems come from errors in my work -- I write a proof of something that (at the time) I think is trivial and later find a counter-example. Suddenly, the problem is non-trivial and interesting.
When I get stuck on a problem? I work on another problem, a related problem, a broader problem, a more specific problem, etc. Anything to try to understand why it is difficult to solve this problem.
