You'd have to wait/sleep a lot or play the game for a very long time, even on the default time scale, in order for your characters to age in any appreciable fashion. Even if that weren't the case there's no way for NPCs to have children or for those children to grow up so implementing other aging/growth/time-based mechanics would result in a world where everyone but recently spawned NPCs are geriatric cases and should be put out to pasture. It'd really break immersion for every town from Chorrol to Anvil to be Florida without the children or vacationing parents. :-/
Stop complaining. I could have done this more painfully. - Dryad from Sacred 2.
I thought your character did age at first, but I guess not.
Still it shouldn't be too hard to implement through a mod or something if you really wanted it. During character creation you have that "age slider" thing, all you would need is a script that moves the slider forward one click every in-game year or so.
I think the longest I ever played an Oblivion character was about a year in game time. I don't think that's enough time for much aging to show, besides all those scars and burns received while exploring Oblivion.
"How ridiculous and how strange to be surprised at anything which happens in life!"