IF YOU HAVE NOT WATCHED "THE NAME OF THE DOCTOR" DO NOT GO PAST THE JUMP.
Here are my predictions. I feel all of these could be true, or just a few of them.
1. The Great Intelligence is The Doctor. First of all, Richard Grant has already played The Doctor in Scream of The Shalka. Which is going to be released on DVD in September. You know, in plenty of time for new Who. So, you know. There's a clue. We also know that at some point, The Doctor becomes The Valeyard. And we know that when The Great Intelligence entered The Doctor's time stream, he fractured into a million pieces... just like Clara, who experienced birth, life, and death in several time lines. So, we could have very well seen The Great Intelligence growing up as a child and dying as a man in that snowman episode, while still being an incarnation of The Doctor.
2. Clara is also The Doctor. She entered his time stream, and went to a place where only The Doctor existed. But she was there. See also, the fracturing into a million pieces thing.
3. John Hurt's version of The Doctor is an alternate timeline Nine who got trapped in the Time War. Because how would that not be the most fucking amazing thing you've ever heard of?
Now, if you will excuse me, I need to rewatch "The Name of The Doctor" then a marathon of 6th Doctor episodes. And I will eat all the cereal in the world.