Me, I'd probably be the dad from Hungry Earth/Flesh and Stone. Well meaning, good guy who gets vivisected in the first of the two-parter episode. I survive, but I'm never really the focus. How about you? Are you a Time Lord? A Companion (temporary like Jack, or permanent like Rose)? An Evil Alien Bent On Galactic Conquest? I WISH TO TAKE THE PULSE OF NERDFIGHTERIA! :D
In real life, I'd be Romana, an intellectual equal to the Doctor, but from the new series, part like Donna, or at least the Doctor-Donna. His intellectual equal, but not remotely romantically interested in him. Just his best friend, who stops him when he needs stopping. So I guess, a mix of Romana and the Doctor-Donna.
Though, what I'd want to be... wait, no. Best friend/intellectual equal all the way!
I would be the companion that the Doctor saves, and then try my best to be an okay companion. Kinda like Martha, but no "why doesn't the Doctor love me" stuff. And I would probably be an alien from some were.