Some games, particularly RPGs, have timeskips. That could sort of count as aging
Also, I feel it should be mentioned that Dungeons and Dragons has an aging system. As you reach certain age milestones (which varies by race), their physical stats (strength, dexterity, constitution) go down (natural decay), while their mental stats (intelligence and wisdom) go up (experience). This has the hilarious side effect of
increasing your vision and hearing, because spot and listen checks are wisdom-based.
It even accounts for magical aging in that magical aging affects only your physical stats.
Oh, and some games, like Neverwinter Nights (which is incidentally based on D&D) let you state how old your character is at creation. This has absolutely no effect on gameplay, but it does let you be a 9999-year-old human fighter with a black ponytail.