Hmm, just to add some missing notes...
-Chu Chu Rocket is another fantastic GBA game. You can no doubt get it for cheap now (well, cheaper). It's one of the best puzzle games I've ever played, and not to mention the one with the most replay value.
Essentially, you lay arrows to guide mice to rockets (specifically yours), and away from cats. These cats can be sent to other players rockets to destroy some of their mice, too. Whoever has the most mice...wins. Very simple. Until you add in players trying to screw you over by placing their arrows against you, or someone gets a powerup (which occurs when a special mouse enters your rocket) and mice flood the board, or maybe kittens. Or maybe gold mice (worth 50 mice). The multiplayer (which is single-cartridge) is, by itself, worth the purchase, because it is extremely intense and fun.
Also worth noting is puzzle mode, in which you get a limited amount of arrows to get all the mice on screen to the rocket, without a single death. There are thousands of puzzles, and you can also make youjr own! In fact, you can also make your own sprites to replace the chu-chus (the mice). And anything you create, you can also give to other owners of the full game via a link cable. It's one of the best GBA games ever, and certainly worthy of every cent you put into it.
-Advance Wars and Advance Wars 2 both include single-cartridge, single-GBA modes. This mode is just as good as having multiple copies of the game, except you have to hand the GBA off. You can even play fog-of-war with this, if you have honest enough friends (though the same can be said for multiple-GBA mode). Advance Wars 2 is, btw, far and away the better game, with many more CO's, though only one new unit does suck.
-Tactics Ogre is a must-have, as is all the Castlevania games and Metroid Fusion.