In Fable and its sequels, the player will become older through game mechanics.
In Fable and Fable: The Lost Chapters, the player begins as a child. During the Oakvale and Guild training sequences, the player will age as the plot progress. The Hero of Oakvale's age can be seen on the Statistics screen.
After the completion of the Guild training the player's age is mostly in the hands of the player. Each time a skill is increased the player's age will also increase (0.7 years per skill increased).
Fable II Modifier
In Fable II, ageing doesn't really seem to affect the Hero much. The major aging difference is from Childhood to adulthood. The next chance to age is by holding onto the Dark Seal, but you will change back to normal when you're done with the main quest. Ageing is also reversible by donating to the Temple of Light or sleeping at Castle Fairfax. Also after you get back from the Spire you may look a bit older, but not much.