Arya kills all the enemies she wants. I'm torn on the idea of her using Tyrion's face to kill Cersei. Part of me can see that happening, but another part thinks that's kind of cheesy. Wouldn't shock me though. But I think Arya is dead by the conclusion.
Stannis dies a heroes death. But no one will ever know it. Like the Halfhand told Jon, we die heroes out here for all of them down there, but no one will ever know it.
Davos becomes the major political force behind sweeping the Starks back into power in the North. The Great Northern Conspiracy theory isn't a true theory, but isn't far off either in the books, difference being Davos orchestrates much of the political posturing with the Northern Lords. Rickon becomes Lord of Winterfell.
Cersei tries to burn King's Landing as Jon Snow and forces approach. Jaime stops her by plunging a sword into her back mirroring the events from the Rebellion.
Robert's "I have a son, you have a daughter, we'll join our houses" line has made me wonder about Gendry and Sansa. Not sold on that though, but something to keep an eye on.
At some point another wedding take place that features the Freys and Boltons, and The Others burst in and rip the living shit out of everything that moves, which confirms the idea that "Winter is Coming" is a not a warning but a boast from House Stark. The Others are the ones who remember.
Speaking of Jon Snow, Tyrion is the connecting factor leading to Jon and Dany meeting. And I do think they will have a son together, and I think Dany will die birthing it. And part of the bittersweet ending is Jon Snow's son...has no mother.
Basically I think Jon Snow = King. As far as Hand, I'm really not sure. Three main choices I think. Tyrion, Davos, Sam. I lean towards Davos, as Tyrion goes back to Casterly Rock, and Sam becomes The Grand Maester.
The bittersweet ending is Jon Snow is King, but doesn't want it, is once again alone and lonely, and with an heir who is motherless, his worst nightmare. His family is mostly dead, his new family is now mostly dead and King's Landing post war is just as cold, bitter, and lonely as Castle Black.