So recently I have seen the theory that Bran is himself the Three-Eyed Crow who appears in his dreams because when he asks Bloodraven about it, Bloodraven doesn't seem to know what he's talking about.
"Are you the three-eyed crow?" Bran heard himself say. A three-eyed crow should have three eyes. He has only one, and that one red. Bran could feel the eye staring at him, shining like a pool of blood in the torchlight. Where his other eye should have been, a thin white root grew from an empty socket, down his cheek, and into his neck.
"A … crow?" The pale lord's voice was dry. His lips moved slowly, as if they had forgotten how to form words. "Once, aye. Black of garb and black of blood." The clothes he wore were rotten and faded, spotted with moss and eaten through with worms, but once they had been black.
But when Bran visits Jon in Jon's dream, Bran is aware of it having happened. (Although Bran never mentions he appeared as a tree not himself.)
This has given rise to theories about who the Three-Eyed Crow "really" is. I have seen people suggest Old Nan (great, love that for her, but she does say all crows are liars so???) or Future!Bran himself (love this less; why would he appear as a crow? And also hated that the show referred to him as such like it was a title not a metaphor).
I tend to think Bloodraven is just really old and it's still likely that he is the Three-Eyed Crow even if he doesn't remember talking to Bran. He's in so many trees and so many times.
But the idea of it being someone from the future is worth considering [Cut for length]
Bran does seem to be beginning to have the ability to speak to people in the past as witnessed by the scene with Ned:
..But then somehow he was back at Winterfell again, in the godswood looking down upon his father. Lord Eddard seemed much younger this time. His hair was brown, with no hint of grey in it, his head bowed. "...let them grow up as brothers, with only love between them," he prayed, "and let my lady wife find it in her heart to forgive..."
"Father." Bran's voice was a whisper in the wind, a rustle in the leaved. "Father, it's me. It's Bran. Brandon."
Eddard Stark lifted his head and looked long at the weirwood, frowning, but he did not speak. He cannot see me, Bran realized, despairing. He wanted to reach out and touch him, but all that he could do was watch and listen. I am in the tree. I am inside the heart tree, looking out of its red eyes, but the wierwood cannot talk, so I can't.
This combined with the fact that we know Bran tells Hodor to "Hold the Door" and this becomes his life's mission or whatever, does suggest Bran will have the power to influence the past at some point.
But I'm still stuck on the idea of why he would appear as a crow. Jojen says he appeared in his dreams as a "winged wolf."
The only person we DO know to appear in dreams as a crow is Euron Crow's Eye. He appears to the Ghost of High Heart as "a drowned crow with seaweed hanging from his wings." There have been theories that Euron is also a warg. He speaks to Victarion of dreaming he could fly, linking him to Bran:
Perhaps we can fly. All of us. How will we ever know unless we leap from some tall tower?
So I suppose a case could be made that it is Euron.
But that... doesn't seem right. The Three-Eyed Crow seems to be helping Bran and I don't know why Euron would unless there was something to be gained from making Bran Stark super powerful. I don't see what that is.
My theory with Euron is that he's drinking so much shade of the evening he's seeing a lot of "dreams" and prophecies he doesn't understand. He saw Dany hatch dragons. Maybe he saw Bran fly too?
Here's my tinfoil hat theory if it's not Bloodraven: Jon.
He's a crow as a member of the Night's Watch. He has two eyes in real life, and one third eye in dreams. (Whereas Bloodraven only had one eye in life.) We know he and Bran can speak to each other in dreams already. It'd be kind of fun if Bran was the one to open Jon's third eye and then Jon was the one to open Bran's. A loop.
And I'm not sure how dying is going to affect his abilities. Maybe he rises more powerful? (That is a thing with several of the gods in this universe: the Ironborn, Azor Ahai being reborn?)
We know there are weirwoods in the Wall, as witnessed by the Black Door in the Nightfort, maybe Jon hooks up with a weirwood there and starts reaching out to his brother.
Another option is Benjen Stark,also a member of the Night's Watch. There's a popular theory died--killed by Craster--and is living his second life in Mormont's Raven. I kind of like that (but also think Mormont himself should be in Mormont's raven, so maybe it's crowded in there? Bran is able to warg into an animal another person is in though so not impossible.)
What if he's alive but down in the trees with the Children as well? Bran says there are others. Most are old, but who knows?
... but I still sort of think it's just Bloodraven. That's just where I'm at.