Darvond: There's an entire martial art ingame: Kisat Dur.

dtgreene: I could also mention that some of the early Final Fantasy games make unarmed combat viable. Specifically:

FF1: Monks (Black Belts on NES) are weak at first, but eventually outdamage everyone else. It's even possible for a monk to kill the final boss in one attack! (In GBA and later versions, which have been rebalanced, Monks start out good and get even better.)

FF2: Unarmed combat is treated as a weapon skill. Really good early on, but lacking in the long run. Equipping a shield will cut your unarmed attack power in half, but I actually do recommend doing so because of how important evade % is in this unbalanced game.

FF3: Two jobs can fight unarmed, but will usually be using nunchucks or claws.

FF4: One character (Yang) can fight well without weapons, but will usually be using claws (but he still gets his unarmed attack power).

FF5: Monks can, again, fight decently without weapons. Works best earlier on; later on, will be less effective unless level boosting effects are used.

toxicTom: ^This. Being a Kung Fu action RPG it has some weapons later in the game, but most of it is classic fist fighting Hongkong style.