Now that I think about it, the first song I managed to learn to play by ear was Chrono Trigger, on the ol' trumpet when I was in high school. T'was pretty awesome, especially since a goodly number of my fellow band geeks knew the song, and occasionally joined in. Getting the Jazz Band going with World Revolution (also CT, for any who might wonder) was also quite the fun time.
Apart from those, the usual fare - Super Mario Bros. 1-1 and 1-2, plus the underwater theme. Haven't done much of it since high school, now that I think about it. Too many things to do, too many instruments around to pick one to play, and too many goddamn noise-nazi neighbors. Hard to blast some SNES goodness on the brass when anything over 90db pisses off the guys around you.