Sigma Star Saga is an awesome GBA shooter / RPG hybrid developed by WayForward. Highly recommended!
Came into this thread to make sure Gunstar Super Heroes was mentioned, left satisfied.Off the top of my head, a couple good arcade compilations that haven't been mentioned yet are Arcade Classic No. 3: Galaga / Galaxian for the Nintendo GameBoy and the Namco Museum 50th Anniversary for the Nintendo GameBoy Advance. I also wholeheartedly agree with just about everything mentioned. Finally, while it's classification as a pure shooter may be up for debate, I have to recommend you try Gunstar Super Heroes for the Nintendo GameBoy Advance; simply put, it's just incredible.
Darius
The GB Darius is actually a remarkably good port.
Was there a US release of Darius, or Japan only ?
Quarth on the original GB is a neat shooter block-puzzle hybrid.
Project S-11 for GBC is worth checking out. It's not the greatest shooter ever, but I think it's pretty good given the GBC's limitations.