^The Great Intelligence/Simeon referenced the Valeyard as one of the more malevolent names the Doctor is known by. "The Doctor lives his life in darker hues, day upon day, and he will have other names before the end. The Storm, the Beast, the Valeyard."
Smith is not the 13th incarnation of the doctor. he merely used up all his regenerations. I get tired when people say hat Smith's number 13. In the Stolen Earth when David Tennant regenerated into himself, he used up a "packet" of regeneration energy but he didn't become a new incarnation. The whole point was he would remain the same incarnation.
That depends on your definition. If you define "incarnation" as a distinct appearance and personality, then Tennant only counts as one. But if you define it as one of the 13 distinct lives a Time Lord gets, then Tennant counts as two incarnations that simply happened to be identical.
Smith is the Eleventh Doctor in every way that matters, but we now know that he was the twelfth distinct personality and the thirteenth distinct life of the Doctor. Those are all simultaneously true, but the latter two aren't particularly relevant except where the past two specials are concerned. So it's really not that big a deal in the grand scheme of things.
Well, given what we got:
Eighth Doctor
War Doctor (Ninth incarnation)
Ninth Doctor (Tenth incarnation)
Tenth Doctor (Eleventh incarnation)
Meta-Doctor (Twelfth incarnation)
Eleventh Doctor (thirteenth incarnation)
If we take things strictly by incarnations, then it has to be between the Meta-Doctor and the Eleventh Doctor... but its highly dubious, because the War Doctor didn't call himself the Doctor during the Time War, thus no one would REALLY know that the Doctor had thought in it other than key people that would know and, of course, the Daleks. Furthermore, its also dubious that he'd be aware of the Meta-Doctor, since he left for Pete's World almost as soon as he came to exist.
Yeah, I think the Valeyard issue, at this moment, is a bit of a mess...
Well guys, here's my take on it:
William Hartnel: 0th regeneration, 1st incarnation, 1st doctor (cycle 1)
Patrick troughton: 1st regeneration, 2nd incarnation, 2nd doctor (cycle 1)
Jon Pertwee: 2nd regeneration, 3rd incarnation, 3rd doctor (cycle 1)
Tom baker: 3rd regeneration, 4th incarnation, 4th doctor (cycle 1)
Peter Davison: 4th regeneration, 5th incarnation, 5th doctor (cycle 1)
Colin Baker: 5th regeneration, 6th incarnation, 6th doctor (cycle 1)
Sylvestor McCoy: 6th regeneration, 7th incarnation, 7th doctor (cycle 1)
Paul McGann: 7th regeneration, 8th incarnation, 8th doctor (cycle 1)
John Hurt: 8th regeneration, 9th incarnation, war doctor (cycle 1)
Christopher Eccleston: 9th regeneration, 10th incarnation, 9th doctor (cycle 1)
David Tennant: 10th and 11th regeneration, 11th incarnation, 10th doctor (cycle 1)
Matt Smith: 12th regeneration, 12th incarnation, 11th doctor (cycle 1)
Peter Capaldi: 13th regeneration, 13th incarnation, 12th doctor (cycle 2)