During the Brain of Morbius story (which was the only old series story that was given a "not for children" rating in Australia, and had to be aired the first time in an after 9pm timeslot) there was a scene in which Morbius and the Doctor fought a "mental degeneration" battle, a video screen displayed each of them as they forced each other "backwards" through numerous previous regenerations. This showed that the Doctor has already enjoyed many, possibly dozens, or regenerations.
But then yes, they later did talk about 12 regenerations. You can't take any of that as pure gospel as obviously there are inconsistencies with a show that has been produced over a 44 year time span.
Long live the Doctor - all of them.