Informal music notation. Existing systems are fine enough for formal classical notation, but if you want to make a quick rough sketch (e.g., lead sheets in The Real Book) it's pretty cumbersome, and the amount of time & effort it takes doesn't seem commensurate with the sort of document desired.

I've been pondering this off and on for years; I think it might require a pretty fundamental switch in how the data is entered. So far the best I've come up with is, uh, pen and paper...