In the season 3 finale, The Master suppressed the regeneration ability of The Doctor and increased his age to millions of years.
From The Sound of Drums episode transcript:
MASTER: Laser screwdriver. Who'd have sonic? And the good thing is, he's not dead for long. I get to kill him again!
DOCTOR: Master, just calm down. Just look at what you're doing. Just stop. If you could see yourself.
MASTER: Oh, do excuse me. Little bit of personal business. Back in a minute. Let him go.
DOCTOR: It's that sound. The sound in your head. What if I could help?
MASTER: Oh, how to shut him up? I know. Memory Lane. Professor Lazarus. Remember him and his genetic manipulation device? What, did you think that little Tish got that job merely by coincidence? I've been laying traps for you all this time. And if I can concentrate all that Lazarus technology into one little screwdriver? But, ooo, if I only had the Doctor's biological code. Oh, wait a minute, I do.
(He opens a large metal briefcase.)
MASTER: I've got his hand. And if Lazarus made himself younger, what if I reverse it? Another hundred years?
(The Master aims his screwdriver at the Doctor, who goes into rapid convulsions. Jack revives with Martha next to him.)
MARTHA: I can't.
JACK: We can't stop him. Get out of here. Get out.
(Lucy is looking very unhappy with all this. The Master stops zapping the Doctor, who now looks at least a hundred years old.)
From Last of the Time Lords episode transcript:
MASTER: What if I suspend your capacity to regenerate? All nine hundred years of your life, Doctor. What if we could see them?
(The Master retunes his screwdriver and zaps the Doctor again.)
MASTER: Older and older and older. Down you go, Doctor. Down, down, down the years.
(Finally the convulsions end. The Doctor is no longer sitting in the wheelchair.)
(A tiny creature with big eyes, rather Gollum-like, peers out from the otherwise empty clothes.)
Yes, The Doctor survived.