Baten Kaitos: Eternal Wings of the Lost Ocean (Gamecube) has one of the most engaging combat systems I've ever played. The whole thing works a bit like poker, a bit like an inventory based adventure game, and a bit like a JRPG.
Basically, all weapons, items, "attack" or "defense" commands, etc., are cards. You build a deck before the battle, so if you want a defensive mage, skip physical weapons.
The most simple form of combo is the straight, with the cards' numbers making a sequence. But it goes so much further than that. For instance, if you cast combinations of cards, they'll form different attacks: enchanted weapons, uber spells, stuff like that.
Even stranger, if you attack someone with the right sequence of cards, it'll create new items. So, hit them with a Kettle, throw Rice in their eyes, throw boiling water on them and slap them with a huge fish, and at the end of the battle, you've made dinner on their face and can walk away with a nice new health item.
Even more insane, though turn based, the game has a real time clock, with Bananas slowly rotting, ice slowly melting (making ice magic hard to do), and all kinds of weird stuff.
But my favorite of all, you don't get gold from enemies. Instead, you need a Camera card, which you use to take in-battle pictures (sacrificing a chance to attack) and sell the pictures off like you're Peter Parker or something. Yes, it's a photojournalist-based economy. The best time to take a picture is right after a melee attack, when you're nice and close.
"Die... why won't you die! ...say cheese!"
No, the game's not in Japanese; Yes, that party member looks like a fairy princess; no, you can easily replace her with a ninja or psychotic fisherman like I did. For me this game isn't about character design so much as a really interesting battle system that keeps me on my toes, rather than the usual attack/spell/heal menu system rut.