If I were to try my hand at any then it would be the Yang-Mills one -- closest to my field. But there are more than six problems to solve, and I'm tackling other ones.
I can remember Fermat's last theorem at uni but that's not on Jim's list, has that been solved now? The beauty of FLT is that it's at least easy to understand the problem. With most of the others, it takes a lot of work to even understand it let alone actually solving it!
http://en.wikipedia.org/wiki/Fermat's_Last_Theorem
The surprising thing about the FLT is that for all its fame and difficulty, the proof runs to only half a page or thereabouts. It's just that to get to that position of brevity you had to prove an even tougher result that took 300 pages of effort or so.