I like good story arcs with significant story elements. Game of Thrones has that in spades. When I first saw season 1, I figured it would make total sense from a story technical perspective if Jon was Daenerys' brother. Why? One was a fire godess on one edge of the world, the other was an ice warrior on the exact opposite edge of the world. These two would eventually meet to do something significant, but since bloodlines always seemed a core concept of the series, I figured if my theory was correct, they'd have to be related as well.
Being somewhat right about that made me feel great. Until I discovered I was about so many other things. So I decided to write down my theories so I can have a good laugh about how wrong I was afterwards, or possibly be surprised by being right. I thus intend to look this stuff back up after season 7 and most importantly season 8.
I'm ordering these from most likely to be somewhat correct, to probably wrong but making sense to me.
Daenerys and Jon form the force against the Night King with the help of Bran
As I explained earlier, I think there are two unmistakably significant themes in Game of Thrones (or rather a Song of Ice and Fire). The clash of fire against ice is the easy one. The importance of bloodlines is the other.
I believed that Daenerys and Jon are related and we have seen confirmation of that in the latest season. In my loose interpretation, the clash between fire and ice will be between Jon, Daenerys and Bran against the Night King and his army. Daenerys will supply the army to this fight: her legion of followers and her dragons. Jon will be the warrior on the ground that leads those forces to victory and he will be the only one capable of actually destroying the Night King in combat with the help of Bran who will act as a catalyst of some sort.
The Night King is a Stark
As bloodlines are incredibly important to the story from my interpretation, I believe the reason this trio are the only ones capable of stopping him is because they have blood ties. I believe the Night King has Stark blood. There will be some sort of reason why he can only be killed with someone who shares his blood. It would make sense to me if a sacrifice of some sort was involved. I fully expect Jon to die when the series ends, or perhaps absorbing the Night King's power and then committing suicide before he generates the same thirst for death.
Bran built the Wall
I could be totally wrong about this, but I thought I gathered that Bran was named after Bran the Builder, a Stark who unsurprisingly built a lot of things, including things for the Night's Watch. I believe he was mostly responsible for the Wall and I think that since we have seen that Bran can manipulate things in the past, he is actually the one that built the Wall in a cycle theory. He goes back into time and makes sure the Wall gets built. This would connect with my next two pieces of speculation.
Bran is the old Three-Eyed-Raven
Yeah, here is where it gets into 'this probably isn't it' territory. But it could be that the old man in the tree is actually old Bran. This is the least fun theory as it is pretty rote at this point to have this type of cycle-story. Nevertheless, it is a possibility I have been thinking about. Perhaps the Night King can never truly be defeated. Whether he can only be suppressed for thousand years or a new one will be born; it is consistent with the timespan noted in the series. The White Walkers were sleeping/hiding for a thousand years. The old Three-Eyed-Raven was waiting for Bran for a thousand years.
At the end of the series, Bran could climb into a tree and wait for a thousand years for the next Bran to teach him how to defeat the Night King. After which that Bran will then wait for a thousand years for the next one and so on. While these stories are played out to a certain extent, I feel it could probably still make some sense and work. I kind of hope this isn't what it turns out to be though. Between Mass Effect, BioShock Infinite, The Matrix and whatnot, while I enjoyed each and every one of them, I don't have too much desire to see one of these types of conclusions again.
Bran is the Night King
I wrote this down, I'm not even sure why I thought this was a legitimate possibility. Looking back at it now, this doesn't make too much sense. I believe I connected Bran and the children, the creation of the Night King and the children and then taking the possibility of a cycle-theory and running with it. Contrary to the previous cycle-theory, this one doesn't make too much sense though.