Hartnell was the first. There are supposedly 12 regenerations, a total of 13 bodies. The fifth Doctor says categorically in Mawdryn Undead: "I can only regenerate twelve times. I have already done so four times."
However, all bets may be off following the Time War. It's never been certain if the 13 body limit is a biological or a legal constraint. With no Time Lords left to enforce it, we don't know what might happen to the Doctor in the future. The 11th Doctor has already suggested that he can regenerate 507 times - though he may have been joking.
Then again, to complicate things further, I should probably also mention this: