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It's not exactly the character model, but this comes to mind.

Of course, inspired by the Doom Guy portrait.

I always wanted an ageing and scar mechanic in Oblivion and similar games, but then I realised, that I would spent hours in creating my character, only to play it for an hour before it gets ugly, because it got an arrow in the face. Then a few hours later I would play an old man/woman for the rest of the game. So...nope.

You age and can get battle scars iirc in Sid Meier's Pirates
In Fallout 2 if you spend too long boxing the Masticator he'll bite off your ear and leave it in your inventory. That results in a permanent -1 to charisma.

And the Sims from the second game onwards of course. Can't remember if there was aging in the first game, except for babies -> kids that is. Didn't really like the mechanic in Sims 2 though. I ended up doing 'quests' or something to repeatably use that fountain of life thing to effectively make my dude immortal :P

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Batman Arkham Asylum (and I'm assuming the later games in the series) had your clothes and cape slowly degrade throughout the game as you got beat up.

I never really liked the visual character mechanics in Fable. I chose to wear black, so then suddenly I'm an evil character and my hair is falling out and flies are buzzing around my head and my eyes glow red? ...WUT?

Would be cool to have a quest to find the fountain of youth, before you die of old age. But then again you would play a few hours as old person, before you get young again and stay so for the rest of the (open ended) game.

As far as I know there exist an ageing mechanic in the Might and Magic and Wizardry RPGs. It's not visual but the age has effects on the stats of your characters. And in Severance: Blade of Darkness and Die by the Sword one can see the wounds on the character.