I'll probably get shot to pieces for this but... I love the Pokémon games.
I've completed Pokémon Red and it was hella good fun. Pokémon Gold and Silver look quite good also. Don't forget to try the brilliant Legend of Zelda: Links Awakening. There's also a little known game called Tetris which I've heard is quite addictive. lol.
Ack. Akira just listed one of my favourites!! Mario Tennis (GBC) is fecking brilliant! God I've not played that one for a few years. It really is super addictive and great fun.
Looks like the recent Amiga game "Payback" is coming to the GBA. Looks really good.