I use to do this when I was working on my prob/stats masters -- sometimes at night, sometimes while doing something "recreational" -- and it is wise to follow up on the inspiration when it comes. A couple of times I ignored it and spent a great deal of time "reconstructing" the insight, if it could be reconstructed at all.

Right now, though, the problems I face are seldom of the form that sudden insight plays any real part in their resolution. Now that I think about it, that's just a shame :(