One of the things I value the most in people is an ability to solve problems. It's actually a combination of a value and a number of abilities.

The value is the desire to eliminate problems; many – if not most – people don't feel the discomfort of walking by a problem without addressing it. If problems don't bother you, you will not be motivated to find solutions.

The abilities include:

Being able to see the problems in the first place
The conceptual ability and the creativity to see connections between the problem and everything that you know, so that you can discover a solution
The ability to push through to solve the problem. Frequently this means trying various alternatives, getting to the right answer with trial and error

Despite people increasingly tagging themselves as "problem-solvers", I think the ability to solve is actually pretty rare. It takes someone who is just a little obsessed, just a little bit of a perfectionist, has just the right amount of patience (enough to try various solutions, but not too much so they don't get bothered by the problem in the first place), and a lot of determination.