The Ninth Doctor was 900 in Aliens of London:
ROSE: You're nine hundred years old.
DOCTOR: Yeah.
The Tenth Doctor claims to be 903 in Voyage of the Damned:
DOCTOR: I'm the Doctor. I'm a Time Lord. I'm from the planet Gallifrey in the constellation of Kasterborous. I'm nine hundred and three years old and I'm the man who's going to save your lives and all six billion people on the planet below. You got a problem with that?
The Eleventh Doctor says he's 907 in Flesh and Stone:
AMY: (She pins him against the Tardis and tries to undo his shirt.)
DOCTOR: Amy, listen to me. I am nine hundred and seven years old. Do you understand what that means?
AMY: It's been a while?
DOCTOR: Yeah. No, no, no. I'm nine hundred and seven, and look at me. I don't get older, I just change. You get older, I don't, and this can't ever work.
After The God Complex he drops off Amy and Rory and spends 200 years travelling. He doesn't come back to them until The Impossible Astronaut in which he invites his younger self and stages his own death. It's at this point that he gives his age as 1103:
AMY: And since when do you drink wine?
DOCTOR: I'm eleven hundred and three. I must've drunk it sometime. (He takes a swig from the bottle and spits it out.)
DOCTOR: Oh, why it's horrid. I thought it would taste more like the gums.
AMY: Eleven hundred and three? You were nine hundred and eight the last time we saw you.
By A Town Called Mercy he gives his age as 1200:
DOCTOR: We evacuate the town. Our ship's just over the hills, room for everyone. I'll pop out, bring it back here, Robert's your uncle.
AMY: Really? Simple as that. No crazy schemes, no negotiations.
DOCTOR: I've matured. I'm twelve hundred years old now. Plus I don't want to miss The Archers.
By The Day of the Doctor he admits to not really knowing his age, and estimates it to be "1200 and something":
WARRIOR: How old are you now?
DOCTOR: Ah, I don't know. I lose track. Twelve hundred and something, I think, unless I'm lying. I can't remember if I'm lying about my age, that's how old I am.
In The Time of the Doctor we first see Clara tricked by the Doctor,and the TARDIS takes her away from Trenzalore. However, she grabs hold of it and delays it's return by 300 years, making him 1500ish:
(There is the sound of a wheezing time rotor.)
BARNABLE: What is it? What's that noise.
(The Tardis is trying to materialise.)
DOCTOR: Well. Where have you been for three hundred years? Ha!
The Doctor tricks Clara again, and she is sent away in the TARDIS. At least until Tasha Lem pilots it back and brings Clara to the Doctor 600 years later, making him 2100ish at the time of regeneration.