1. White Walkers
Bran Stark is the key to the White Walkers coming beyond the Wall.
We know that the Wall was built (by Bran the Builder) with a sort of magic that kept the White Walkers out of the North and the rest of the Seven Kingdoms, but in Season 6 episode 5, Bran is touched by the Night King in a vision. When Bran reveals his arm, there is a blue frost mark on it from where he was touched. The three-eyed raven says that because the Night King touched him, the cave they were sheltering in would no longer protect them, for the magic was broken. The same magic, I'm assuming, that is on the Wall protecting everyone.
If Bran crosses the Wall with Meera Reed, then the Night King and the White Walkers can finally cross the line too. This is also evident when Benjen Stark tells Bran that he cannot cross the Wall because the magic does not let those undead cross. As Benjen was attacked by White Walkers and saved by the Children of the Forest, he cannot cross either.
Will we see another "oops" moment from Bran? Or will there be another way the White Walkers will be coming over for the party?
2. Bran's Knowledge on Jon Snow
Is there a chance that Bran will be the one to reveal Jon's lineage to him?
In Season 6 episode 10, Bran and Meera stop at a Weirwood Heart tree before continuing their journey over the Wall. Bran touches the Heart tree and has a cluster of visions before stopping at the Tower of Joy where he sees his young father, Ned Stark, climb the tower reaching his aunt, Lyanna, at the top. Bran seees that she is dying after giving birth. He hears Lyanna plead with Ned:
"His name is [...] If Robert finds out, he'll kill him. You know he will. You have to protect him. Promise me Ned. Promise me."
Bran realizes in this scene that the baby of his aunt Lyanna and Prince Rhaegar Targaryen is his alleged half-brother, Jon Snow. Lyanna pleads with Ned to protect her son because if Robert Baratheon, her original future husband, found out about Jon, he'd kill him. Because Ned's honor was deeply rooted within, he agrees. Thus finally bringing peace and truth to Ned's history of "cheating" on Catelyn and bringing home a bastard son during Robert's Rebellion. When we now know he brings home his nephew.
If Bran gets to Jon before any other theory plays out about Jon finding out, there's a chance that Bran will be the one to reveal Jon's lineage to him.
*It should be noted that it is unknown at this time whether Bran heard Jon's true name being said during the vision when it was muted for the audience.*
In Season 6 episode 5, Bran watches in his vision at Winterfell that a boy named Wylis at the stables has a seizure that Bran unknowingly caused. Wylis was changed into Hodor when the past Hodor heard the future Meera shouting "Hold the Door". Hodor heard the phrase, had a seizure by repeating what he heard in his head and was mentally disabled. This happened as a result of future Bran accidentally warging into his younger self during a vision. Why does the matter, you may be wondering?
Throughout the series, King Aerys II Targaryen, Daenerys' father, was referred to as the "Mad King". We know that he was stabbed in the back by Jaime Lannister during the Sack of King's Landing. However, what we don't know is what made him "mad" in the first place. I'm thinking that Bran easily could've been the reason that Aerys went insane. Jaime Lannister says the Mad King kept screaming what he'd been screaming for hours, "Burn them all." Maybe Bran went back in time with his visions and tried to tell King Aerys II about the Night King's army, maybe by saying he needs to "burn all the wights and the Whtie Walkers" to save Westeros and in turn accidentally changed Aerys the way he changed Hodor.
We've been learning that only fire will destroy a wight and dragonglass or Valryian steel will destroy a White Walker. "Burn them all."
4. Dragon Rider
In Season 1 episode 1, Bran was tragically pushed out of a tower window by Jaime Lannister and thus made him paralyzed/unable to walk ever again. In Season 4, Bran asks the three-eyed raven if he will ever walk again. The raven tells him, "no, but you will fly." My speculation is that the raven mean that Bran will be able to fly with one of Daenerys' dragons. Bran is a very powerful warg. He was able to warg into Hodor and control him, but he was was also able to train to see visions with the raven. Bran easily could be one of the three dragon riders of legend. There's a chance he could warg into one of Daenerys' dragons. Maybe warg into Rhaegal?
There's a lot we can expect from Bran. He wouldn't have lived this long if he wasn't a key element to the story (and one of my favorites). We'll have to see what this little lord will bring to the table.