BOF II was pretty overpowered with Blue. She is everything Nina is, but better.

And she can regenerate her health...

Outside of optional characters, I'd say Rand is probably your strongest player, though I'm not sure he'd be overpowered. He's an amazing tank, even with his poor equipment. His physical attack is solid, and he's got amazing Healing magic.

In any version of FF IV virutally any problem is solvable by a berserked and hasted Edge, and since you can pull this off without the need of caster due to Items, though even then I'm not sure I'd put this to overpowered.

Though an obviously overpowered character is Wild Arms 3 with Clive. Never improve his guns ammo, the two shots before reload is all you need. Just boost up accuracy, power, and a bit into critical hit. Spend one round buffing him, proceed to kill any boss in 2-3 hits. So 4 or 5 rounds if it's a huge HP boss. Without an attack from anyone but Clive. Really everyone else damage output is so pitiful by comparison there isn't a point in attacking with them.

The Wild Arms PSP game had a guy who could, with 100% accuracy, break any enemies weapon. And virtually every enemy in the game is human, so its effective on probably 70% of the guys in the game. And it works on human bosses.

And in Dragon Age 2, Meril is a smurfing beast.

She, my mage, was the only one of my three companions alive, and this was at the start of a battle the other two were killed. I sat back and watch my Mage be swarmed, and just massacring everything, taking no damage. That should not happen.

In Earthbound, with a couple Bottle Rockets Jeff could take out any boss. So for most battles, Jeff is pretty damned over powered.