Final Fantasy I & II: Dawn of Souls/Final Fantasy IV Advance/Final Fantasy VI Advance - As I discussed in one of my PlayStation posts, Final Fantasy Origins was my first chance to play through the first two Final Fantasy games, but the Game Boy Advance cartridge is probably the best place to play them. The problem with the PlayStation versions is that the CDs have longer load times which becomes a bit annoying going into every single random battle.
Final Fantasy IV Advance benefitted as well from the cartridge format over the disc-based port from Final Fantasy Chronicles. Other additions to the Super Nintendo classic featured a new bonus end-game dungeon, some new gear, and a new localization restoring some of the story elements from the original game that were cut from the original North American release.
Final Fantasy VI Advance is probably the best iteration of my favorite game. Like the games above, the cartridge-based port cut down on the load times that the PlayStation port from Final Fantasy Anthology version suffered. The art was cleaned up slightly (but remains the original Super Nintendo sprites instead of the redesign that came in the mobile/Steam versions of the game). Four new Espers, a few new spells, and two new end-game dungeons fill out this already exceptional game.
Final Fantasy Tactics Advance - The only fully new game in this entry. While drawing heavily from the PlayStation classic Final Fantasy Tactics, Tactics Advance forged a new story and tied more into the lore of Final Fantasy XII, trading in the Zodiac-heavy elements of the original for Totema, Judges, and Law cards that changed the rules of a battle area. Tactics Advance also kept the job system its predecessor, while introducing new species beyond just the human characters of the PlayStation game. Final Fantasy Tactics Advance didn't quite reach the heights (and depth) of the original game, but it was still a good strategy RPG in its own right, worthy of the brand.
Let me know your favorite Game Boy Advance games. I didn't play the system all that much as I was predominantly a console gamer during the systems lifespan so I'm sure I missed some classics.