Gradius 3 was my favorite while growing up, despite the massive slow-down (Boo on the wimpy 4MHz SNES processor). For some reason arcade mode on that thing seemed to have a relaxing effect on me... o_O 30-man code? Bah, for wussies.
Later on, it was StarFox and Super R-Type. I haven't managed to get a hold of a real copy of R-Type 3, but the emulated version I've played is a lot of fun.
I need to get more, obviously. Shmup is my favorite genre.