Kingdom Hearts: Chain of Memories - I neglected to mention the Kingdom Hearts series in my favorite games from the PlayStation 2 list. That was clearly an oversight because combining Final Fantasy and Disney characters was one of the weirdest and most amazing mash-ups of my youth that I never knew I wanted. Chain of Memories was the first spin-off title for the franchise and the only one I ever bothered attempting to play, back before Square Enix went off the deep end in how they name their games and using a random number and word generator.
Kingdom Hearts: Chain of Memories was basically a retread of the events of the original Kingdom Hearts, but now in pared down 2D form. This is justified in-game by having your characters lose their memories and needing to rebuild them by revisiting Sora's initial adventure. While it was still a ton of fun playing through the Square Enix version of so many classic Disney films, the highlight was the combat: an interesting diversion from the hack-and-slash RPG elements of the console games that let the player choose attacks from a deck of cards.
Golden Sun/Golden Sun: The Lost Age - Of the new IPs introduced for the Game Boy Advance, the two I thought would continue long past that system and develop into franchises of their own were Advance Wars (which I actually never played but knew from reputation) and Golden Sun. And while there was Golden Sun: Dark Dawn for the Nintendo DS, it would appear this franchise is mostly abandoned, which is a shame as it could have served as a nice alternative to the Mario RPGs and Bravely Default games of the 3DS, filling out Nintendo's library with a bit more from the traditional JRPG field.
Both games featured beautiful sprite-based graphics. And the Psynergy (this lore's version of magic) served a dual purpose in both combat and through some light puzzle-solving in the overworld in order to find hidden treasures and progress through the story. And as a fan of the classic Final Fantasy games, the Golden Sun Djinn system was a welcome innovation in the vein of Espers and Materia.
Sword of Mana - Sword of Mana was a remake of the Game Boy classic Final Fantasy Adventure (so named to cash in on the Final Fantasy brand). While I never had any of the Final Fantasy Adventure games on my own Game Boy, I often enjoyed playing them on a friend's or borrowing his cartridges.
I didn't realize at the time that Sword of Mana was a modified version of those old games, mainly because they had removed the Final Fantasy branded elements and I didn't quite remember all that much from some Game Boy games I had played only occasionally 10 years earlier. Still, it was a fun enough game in it's own right and I very much appreciated the throwback feel of the game. Finding out years later how the two were related was just icing on the cake.