Dogstar once recommended a game called Gleylancer.
This is my favorite shmup, just because the game actually gives you the option to continually fire without having to hold down the fire button. I think all shmups should do that. Because really, you're playing a shmup, is there any reason you would ever NOT want to be constantly firing?
My favorite obscure Genesis games are both ports of Amiga games published by Psygnosis: Puggsy and Wiz 'n Liz. The Sega CD version of Puggsy is a little better, although it doesn't have enough music.
Puggsy's a puzzle platformer whose main mechanic is the manipulation of dozens of objects in the world to solve the puzzles. It was pretty huge for its time, with tons of secret levels and minigames. Everyone should play it.
Wiz 'n Liz is a totally hyperactive arcade game that's sort of hard to describe. It really is one of the best games on the console, though. Just check it out.