S., for example, asks:
"So - Doctor Who's last 'reincarnation': does that count as a real one? How does this affect the stated limit of reincarnations?Well more fool you.
I want to know."
I don't think this counts as his tenth regeneration; he seems to stop the process mid-way by siphoning off the energy into his discarded hand. The blue-suited Doctor is an amalgam of that energy and Donna, rather than an eleventh Doctor. He can't regenerate, so presumably brown-suited, fully Time Lord Doctor is yet to become the eleventh Doctor. I suppose Blue Suit is Doctor 10a.
But is David Tennant even the tenth Doctor? Ignoring Richard E Grant's web adventure as the ninth Doctor, or even where Peter Cushing fits in, the TV series hasn't always been sure. In The Brain of Morbius (1976) we seem to glimpse images of five Doctors prior to William Hartnell's "first" Doctor - men in Doctorish costume who bear a startling resemblance to various members of the then production team. (Some speculate that these images are not of the Doctor but of Morbius, who is also a Time Lord. I think that's willfully ignoring how the scene plays.)
Yet the Five Doctors (1983) has Peter Davison's Doctor refer to himself as the "fourth" regeneration - so he is the fifth Doctor, whatever the Brain of Morbius might think.
The first we knew of a limit on regenerations was The Deadly Assassin (1976), when the Master has run out of them and is trying to extend his life. It's established that Time Lords regenerate 12 times so have 13 lives. Later in the series the Master steals people's bodies - Anthony Ainley played him in the 1980s, and Eric Roberts in the 1996 TV movie.
The cap on 12 regenerations was also a feature of Mawdryn Undead (1983). But that story was about aliens who had stolen Time Lord technology so they could give themselves the powers of regeneration. Which implies it is something that is "given" to Time Lords, rather than something they are born with. (How Time Lords are born is another long and tricky subject).
And yet later in 1983, in The Five Doctors, the Time Lords offer the Master a "complete new regenerative cycle" in return for his help. Which implies Time Lords can be topped up. Indeed, last year's Jacobi-Simm regeneration seems pretty much identical to the Eccleston-Tennant one, so is presumably the same regular process - implying the Master got new lives. Note that when he dies as John Simm, he chooses not to regenerate. There's no implication that he can't.
Which all means there's an easy precedent for whenever whoever is playing the 13th Doctor decides to do something else. If they even mention the cap on 12 regenerations, the Doctor can just be awarded new lives by the Shadow Proclamation, or find them in a cupboard or something.
That said, the whole point of The Brain of Morbius and The Five Doctors is that eternal life is as much a curse as a blessing, something the new series has made quite a deal of too.
I bet you wish you hadn't asked now.