Kain.
No other character has made me feel such a plethora of emotions in a game. I thought he best carried the overlying theme throughout the game. He was in a constant struggle with trying to redeem himself.
From his unique ability; his jealousy; his struggle with selflessness; and his eventual redemption he was the focus of many plot twists throughout the game and was perhaps the most pivotal character.
I think he's easily the most interesting character in the series.
Commonman makes a pretty solid case for Rydia too.