One of the most common theories is that Thorin is in possession of one of the seven rings of power given to the dwarves by Sauron, specifically the ring that was passed down the line of Durin. In the mythology, that particular ring was in the possession of Thorin's father Thráin but retrieved by Sauron before the events of The Hobbit. So in the book, Thorin never possesses a ring of power at all.
However, the theory is that - in the film's continuity - Thorin did, somehow, manage to acquire the ring of power before his father disappeared. Now, the rings of power that Sauron gave the dwarves did not cause them to fall under his control, but instead essentially allowed him to influence them into becoming more greedy, angry, narcissistic, and arrogant. Howard Shore's decision to use the Weathertop theme (aka the track that is most associated with the Nazgûl) makes sense if Thorin does possess one of the rings.
Thinking back to Fellowship (the film), Aragorn has a line when he's explaining who and what the Nazgûl are to Frodo, "They were once men, great kings of men. Then Sauron the deceiver gave to them nine rings of power. Blinded by their greed, they took them without question; one-by-one falling into darkness". The argument is, that's exactly what's happening to Thorin. In that scene, Thorin gets up, turns his back to his friends and companions, and instead of helping them he gives in to his own personal desire for revenge by charging straight towards Azog. No strategy, no plan, just blind rage. The Nazgûl theme makes sense in this instance because, much like the Nine, Thorin is giving in to the influence of a ring of power. It also explains why he's such a complete dick to everyone.
That is of course all predicated upon the baseless theory that Thorin
does possess a ring of power - which is never mentioned or even hinted at in the film. I do really like it though, so I've decided to just go with it for now
