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, perhaps overrun by ice zombies. 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.
So, he Quantum Leaps into Jaime and throws himself out of the tower, crippling himself and tipping the first domino in the series of events we're all familiar with. Of course, it's entirely possible that George R.R. Martin will read this and then have Bran be eaten by a Sharknado in Book 6 just to spite us.
And while we're looking at crazy time travel possibilities ...