6. He'll Challenge Her Claim
Cersei Lannister sits atop the Iron Throne, but it's a position Daenerys feels belongs to her. She sees ruling the Seven Kingdoms as her birthright, which is of course why she's sailed to Westeros. But will she be successful?
The logical standpoint is yes, even though the Iron Throne isn't really going to matter when the White Walkers come calling. Though Euron gave her an early setback, Dany still has the most powerful armies, and those three grown dragons to totally change the game. Cersei will put up a fight, but it's easy to see Daenerys claiming the Throne from her, and ruling for however long she is able before the real battle begins (and possibly afterwards).
But could Jon challenge her claim? He'd certainly have a case for it. Although he's Daenerys' aunt, Westeros' succession laws favour male heirs, meaning that, typically, his claim would be stronger than hers. Setting this back is the fact he's a bastard, but it could well be proved he was the legitimate child of Rhaegar and Lyanna (if they really did get married), while being a bastard didn't stop him becoming King in the North.
Robert Baratheon ended the Targaryen dynasty and changed the succession, ensuring his 'own' children would sit on the Throne, but Cersei taking it largely means any such succession laws are basically moot. The rightful ruler is now just the one with the power to be, and one thing we know of Jon is that people will follow him.
The easy argument against this is that, even ignoring any notion of succession, Jon probably wouldn't want the Iron Throne, as he's focused on the threat Beyond-the-Wall, and has never wanted to be a leader. But it's that which also makes him a prime candidate: George R.R. Martin has shown he loves a reluctant leader, one who doesn't desire to rule but is well-equipped to do so, and that's Jon Snow, not Daenerys. He's got the same sense of honour as his father, and if sitting on the Iron Throne is what's necessary to protect or save the realm, he's likely to do it.