Rogue Trader said:
Golden Sun is a close second, and all the SNES remakes are pretty good as well (esp. Link To The Past).
I agree
"The Legend of Zelda: A Link To The Past" is the game I'm going to recommenced, I wouldn't say you have to be a Zelda fan to enjoy it, it's quite large for a GBA game, and will take awhile to finish, the story is quite involving and strange like Final Fantasy, but if your into that like I am, than you'll enjoy it. However, I don't recommenced it if you don't like RPG or Adventure games, also if you have a Wii, I would download the Virtual Console version rather than get the GBA version, only because it's in a higher resolution and the controls are slightly better.
Other games I would recommend are:
Final Fantasy V (or any of the others)
Metroid (maybe Zero mission first, to help you get into the series)
Zelda: The Minish Cap (a lot like Link To The Past, but a bit more simple, in fact if you can't get into the LTTP story, then play this)
Baldur's Gate (I never got around to playing the GameCube version, but I know this GBA version was pretty good)
Super Mario Advance 1-4(What can I say? There Mario, imo even though I like them all, I would say SMA2 Super Mario World is the best.
But like Rouge Trader said, the GBA had a great library, this is why Google is your friend.