I wrote an article on playing really old (1000 years or so) characters that used that idea as one of the rationales for how you could start off at first level.
Another way to do this in D&D is to take advantage of the level drain mechanic. My character was a dedicated vampire hunter, until my ageless adversary chose not to kill me, because that would be too easy, but to take away everything I'd ever done, leaving me only with the memories of skills I might never be able to regain in my now-aged body, in these last years of my life.
Come up with some reason why Restoration won't work (curse from the Dark Powers, doncha know) and you've got a character that *remembers* being a bad mofo, but is 1st level like everyone else, just grizzled, weather-beaten and white-haired.
Some settings, such as Ravenloft, or the nation of Geb in Golarion (which has vampires in it's upper class, who keep regular slaves that they feed off of), would have this sort of potential built right into the setting, and the character doesn't necessarily have to be a vampire-hunter, so much as any old adventurer that ran afoul of a vampire (destroying his 1000 year old vampire girlfriend, for instance). This would be a particularly potent backstory for a Cleric. The vampire didn't want to kill you and send you to your beloved sun-goddess, so instead he drained away all of the gifts of faith you'd earned over the last twenty years of your life, leaving you, the former high priest, clinging by a tenuous thread, with no greater spiritual connection to She Who Shines in the Sky than a pathetic acolyte, barely fit to carry candles to light a deacon's way through the sanctum!
Ditto for an 'ex-Paladin' concept. Years of valorous deeds drained away, left a grizzled scarred Fighter who *remembers* being a shining knight, smiting the wicked and ending evil with a charge, on a celestial warhorse. Days from a past he wishes he could forget, because he knows that he'll never be able to climb his way back up that long road. Perhaps another drink of this wine will help him forget...