[jackdawjack]

don't forget the yang-mills mass gap and the navier-stokes initial value problem, both clay millennium problems and both rather important. Well the yang-mills one is probably more important, this list is a bit m-theory biased.

I think the m is originally for membrane, not "magic" but apparently its open to interpretation.

[Maro]

The way those problems are posed, by the Clay Institute, they're more math problems than physics problems. Check out the price lectures on their site to see what I mean.