Game Of Thrones Ending: Predicting What The Books Will (& Won't) Change
7. Daenerys' Death

Jon Snow killing Daenerys is one of the biggest moments of the entire series. While Thrones has a sprawling ensemble, they were the two biggest characters - and heroes, for that most part - and him killing her, whether you liked it or not, is a momentous occasion.
It's so huge, in fact, that it feels like it needs to happen in the books in some way. Jon and Dany definitely need to meet - there'll be some romance too, whether it's falling in love, a political marriage, or one leading to the other - in order to fight the Others, and then to explore the ramifications of his parentage too. Because they're two characters who will make it to the very end, with their stories become increasingly entangled, then it would make sense for Jon to be the one to kill Daenerys, with two possible reasons.
The first would be sacrifice. While the show didn't give it too much attention, the prophecy of Azor Ahai/The Prince That Was Promised is another that's a much bigger deal in the books, and likely refers to one of Jon or Dany. Azor Ahai was able to bring forth Lightbringer by plunging his sword into the heart of the woman he loves, Nissa Nissa, and George R.R. Martin could be setting up something similar with Jon & Daenerys (it'd potentially be interesting to have a reversal of this, with Jon the Nissa Nissa figure, but it's very hard to see him dying twice).
The alternative is that Dany burns King's Landing, then helps defeat the White Walkers, and then expects to simply be Queen. The darkness has already emerged in her once before, and it could do so again: if she saves the realm and it still doesn't love her and, what's more, she discovers after all that there's ANOTHER Targaryen heir with a better claim than her, it could well lead her past the point of no return, and require Jon - who by this point would again have become a key part of her story, and vice versa - to kill her.
At this point, the Nissa Nissa angle feels the more likely, if only because having Dany burn KL, find some redemption against the Others, and then turn back requires a lot of work, whereas there's a clearer setup for the Azor Ahai/Nissa Nissa death, but both are certainly plausible and, ultimately, would involve Jon sacrificing love for duty.