Quoted from InfiniteLives:
any gameboy advance enthusiasts want to give me some titles that might be a bit more obscure but you really dig?
Defiantly get DooM! If nothing else, it's freekin' DooM on a GBA!
And if youy like first person shooters, I'd highly reccomend Ballistic: Ecks vs. Sever
And if you're into Pokemon, Pokemon Fire Red or Leaf Green well worth getting. Their updated versions of the original games, but the adventure extends on beyond the originals.
Puzzle games? Super Puzzle Fighter II, or Columns Crown. It's pretty much a one player version of the Classic Columns, with different music and theaming.
Or if you're a fan of the Dreamcast game Chu Chu Rocket, there's a version for GBA (it was literally the very first game I ever saw for the GBA!)
Platform? Super Mario World Advance