Wrestling games come to mind; expansive character options in terms of both looks and stats which affect the game and even the story.
I also liked the Ogre Battle/Tactics Ogre system where, while not directly affecting your appearance, you were asked a series of morality questions which affected your alignment and starting units and actually had an effect on your story paths (although you could modify your alignment with in-game choices).
Wrestling games come to mind; expansive character options in terms of both looks and stats which affect the game and even the story.
I also liked the Ogre Battle/Tactics Ogre system where, while not directly affecting your appearance, you were asked a series of morality questions which affected your alignment and starting units and actually had an effect on your story paths (although you could modify your alignment with in-game choices).
I was just about to mention wrestling games.
It's been twenty years since Knight of Lodis came out, and I'm still looking for another tactics game that scratches that itch half as well.