It's pretty easy to say what kinds of problems are not interesting: those where instead of solving a few big, clear, problems, you have to solve a lot of nasty little ones. One of the worst kinds of projects is writing an interface to a piece of software that's full of bugs. Another is when you have to customize something for an individual client's complex and ill-defined needs. To hackers these kinds of projects are the death of a thousand cuts.
[1] http://www.paulgraham.com/gh.html