I always liked the idea that not every adventure is a 16 year old. Sometimes the grizzled old farm hand or village priest must go fight evil and find fortune, and who's to say he's too old to go?
At the same time, I never quite liked the "ability score modifier" approach to age. Once the ability scores have been rolled, why modify them right away?
Here's my take:
Youth: Fantasy stories often feature characters in their teen's (and for a medieval setting, that may be "functionally adult" in any event). Youthful characters get the ability to move silent and hide like a first level thief. (actual thieves function as one level higher in those two abilities).
This is pretty useful, but the ability won't scale over time, so it remains an emergency attempt.
Adult: In their prime both physically, and in drive and motivation, adult characters start the game with 1D6 additional hit points.
Mature: As age takes it's toll, experience takes over. Mature characters begin the game with one additional skill (if using a skill system, such as that provided here
If not using skills, simply have the player designate an area of knowledge or expertise and roleplay the effects.
Old: Once you've been around long enough, your skills might start to suffer and you can't run around like a loon all day, but you've been there, seen it before, and those experiences might save your skin. +1 bonus to all saving throws.
Under these rules, Dwarves are always Mature, while Elves are always Adult. Halflings age as humans but slightly slower.