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Watch The Night of the Doctor (above) before reading.
Or don't, but beware that the following contains SPOILERS to the above.
So, let me start by saying:
I WAS RIGHT!
John Hurt is an incarnation of the Time Lord we know as the Doctor, and specifically he is the one who fought in the Time War. Not only that, but he regenerated from Eight (that's who Paul McGann was, for those unaware -- he was Eight in the 1996 made-for-TV movie that was an American production company's failed attempt at reviving the series) -- and he's not Eccleston! This means that, unless there's another one in between we still don't know about, Hurt is Nine, making Eccleston Ten, Tennant Eleven, Smith Twelve, and Capaldi comes in as Thirteen!!
We also have the definitive answer to why Eleven referred to him as "the one who broke the promise" -- he abandoned his name, abandoned his purpose, to join in the Time War. (The credits call him the War Doctor, although I doubt that's the name he's going to go by in Day of the Doctor...)
Tem's suggestion of a connection to Four's (that's Tom Baker, not [private] :-P ) serial The Brain of Morbius is also correct: The Doctor crashes on Karn, the same planet, and even meets up with the Sisterhood of Karn and references the very same Flame of Utter Boredom (er, that should be Eternal Life) that Four restored in that serial.
And, could this be the answer to Moffat's infuriatingly cryptic "go back and count" comment? Does the Flame not just grant life, but restore a Time Lord's regenerations? Is that what Ohila meant by "Time Lord science is elevated here"? Or was she only referring to the Doctor having the ability to choose his next regeneration?
Incidentally, that's a new one entirely, having any choice in the matter. I am a bit disappointed that he didn't at least consider ginger for a moment, though, but I guess he did have more important matters on his mind. Ah well.
I need to get my hands on a copy of the Brain of Morbius, stat, because it seems that that one's going to become rather important!!