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).
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.