The way I understood it was that 3/4 is used to notate waltzes and other music where you are supposed to "feel" all three beats per bar, and 6/8 is used to notate music where you only "feel" the downbeats. Things like swung rhythms. Though (again as I understand it) actual swing music is often notated in common or cut time, but played as though the first eighth note of each beat is about twice as long as the second.<p>Just to pick two of my favorite songs: per my understanding, the opening theme to Vision of Escaflowne would be notated in 3/4, while "Flagpole Sitta" by Harvey Danger might be notated in 6/8.