I've certainly solved problems with a storage scope before, but not for a long time, and they were mostly software problems rather than hardware problems (ie. using it as a poor man's logic analyzer to infer what's going on with the code via a couple of spare IO pins). I really kinda want one though.
A fairly accomplished electronic engineer told me that they'd never once solved a problem using an oscilloscope, but that it helped to keep them occupied while they were mulling over what might have gone wrong. (That's presumably why the better ones have so many knobs and dials to play with, like one of those children's toys.)