Ill go for the lesser known games (and a few well known that no one talks about)
Car Battler Joe - Think Twisted Metal/Carmeggedon, with upgradable vehicles.
Tactics Ogre - The best of the Strategy RPGS on the system (upgradable Chess).
Boktai - A fun little action adventure that requires the sun.
Ecks vs Sever 1&2 - 2 of the better FPS on the GBA.
Gadget Racers - Cutesy upgradeable racing.
Karaaj Ralley - RC ProAM for a new generation.
Zone of the Enders: Fist of Mars - probably the best startegy game on the system.
Super Dodgeball Advance - Think of it as a hybrid of an rpg and a sports game. It was a launch title but it is still one of my favorites and Ive played most of the catalog.
Konami Karts - What MarioKart Advanced wanted to be.
Chu Chu Rocket - Equal to its Dreamcast counterpart, but portable and single cart multiplayer.
Sabrewulf - My personal favorite of the system, an action platformer with a dash of adventure. Grab the treasure from the Sabrewulf and make it back to the begining without him killing you. I did wait 20 years for a sequel to the speccy version so yes I am bias.
The GT Advanced series - very good racers, the first two are rally , the third eludes me.
CT Special Forces 1&2 - Modern day Metal Slug.
Godzilla Domination - King of Monsters skinned for Godzilla.
Iridion II - a decent shump, stay far away from Iridion 3d though.
Lady Sai - a fun little action adventure, in the vein of the modern Prince of Persias.
F-zero GP - the original Fzero on steroids.
Wizards - the sequel to Warlocked on the gameboy, a pretty good RTS
CIMA the Enemy - another good Japanese styled RPG
Imports:
Kuru Kuru Kurin - abstract puzzle game - simply a blast and no real language curve.
Napoleon - A very good RTS
Magical Vacation - the best Japanese RPG on the system hands down.
Famicon Mini - Kid Icarus - because it is Kid Icarus
Bitgenerations - all - they look like techdemos but man are they addictive
Mother 3 - sequel to the US SNES rpg Earthbound.
That should do for now. If you want a better description, or longer list, dont hesitate to ask. Though I cannot tell you when I will reply.