That's actually a very interesting question. You'd want a problem which:

1. is either embarrassingly parallel or large enough to get a decent speedup,
2. involves a fair amount of complex branching and logic, such that GPGPU would be unsuitable,
3. cannot be efficiently solved by "shared nothing", message-passing systems, such as Beowulf clusters and grid computing.

The link also states that the aim should be "to help society, to help others" and to "make the world a better, more interesting place". Here's a start; in fact, many of these problems are fairly relevant to AI.