So insane they could be true!
The young son of doomed hero Ned Stark, Bran, gets shoved out of a tower window after peeping.
Later, the puppet-legged Bran Stark discovers he has a whole host of magical mind powers, including the ability to see his father in the past. He is told he can only visit the past and not influence it, but Bran also has an even mightier super power: He can take control of people and animals for brief periods of time. So, who's to say he couldn't beam his psychic brain meat into someone else's head?
Our favorite is this fan theory posted by a Reddit user, in which a Future Bran is living in a version of Westeros that has been completely destroyed. Through his mental time-traveling abilities, he is able to see an alternate future in which everything turns out (more or less) OK and pinpoint the exact moment in the past when the two realities split: The day he catches Jaime and Cersei up in the broken tower of Winterfell, making each other more nieces and nephews. In his version of the future, Bran was never crippled, and a whole alternate (worse) history played out instead.