If you haven’t seen the show or read the books, be warned:

Sansa
Where we left her in the books: Sansa escaped King’s Landing after the death of Joffrey, Dyes her hair black and arrives with Littlefinger at the Vale as “Alayne Stone” Littlefinger’s bastard born daughter. Liza goes coo coo for cocoa puffs and tries to throw Sansa out the moon door. Littlefinger saves Sansa by pushing Liza out the moon door, and blames the musician who witnessed all this. Littlefinger becomes the regent of the Vale, Promises Sansa that she will marry a young nobleman of the Vale and everyone makes plans to leave the castle before they are snowed in, and that’s it.

Where I think she will go: I don’t think Sansa is dishonest enough to fall for Littlefinger’s logic that “Alayne Stone is not married to anyone” by law she is still Sansa Lannister and she won’t forget that. I don’t think she will go along with being married to anyone else.
Long Term Sansa is in a great position politically. If she can play her cards right with her cousin Robert Arryn, and get Littlefinger to legitimatize her, she will be the rightful hair to the North(as a Stark), The Westerlands (through Tyrion) the Riverlands,(though her Tully blood AND as the hair to Peter Balish) and she can control the Vale of Arryn. Will Sansa take advantage of this power? I like to think she will. I like to think that Sansa will soon become a powerful player in the Game of Thrones.
Bran
Where we left him in the books: Bran is in the cave, learning to control his green sight and warging powers.

Where I think he will go: I think Bran will become more powerful and be able to make small changes to the past. I think he will learn of Jon’s parentage, maybe uncover a few more secrets, and I think he will see the origins of the Others. At some point, for some reason, Bran and Company will need to escape from the Children of the Forest. Hold The Door will happen and I will cry all over again.
Long Term: I don’t know if Bran ever goes back south of the wall. Meera is not going to drag him back to the wall alone. No way, she’d die. if they do make it back, they need help. Coldhands, Uncle Benjen (not the same person!) or some Wildlings could help them. Regardless of Jojen’s fate, the kids need help if they plan to go south.
I do think Bran will try to stop the Others in the past somehow and make things worse. I don’t really see Bran loosing himself to the three-eyed-crow like he did in the show, I think it will still be Bran in there, for the most part. Bran is only seven when the series starts. He’s dealt with more than any seven-year old can and still be a normal happy person. Even if he does walk again, Bran will still be broken.
Sam
Where we left him in the books: Sam has just arrived at the Citadel so that he can become the new maester for Castle Black. He meets Marwyn, Alleras (presumably Obarin’s daughter Sarella in disguise) and Pate (presumably a faceless man in disguise) They not only expected Sam, they want his help with their plan.

Where I think he will go: It’s all going to depend on what this plan is, and how the Citadel reacts to Young Griff’s invasion. I think Sam will study history, learn some plot points (but not secret marriages because that would be stupid) and do what he can to help Danny, because that was Maester Amon’s last lucid goal.
Long Term: I think Sam survives the series. I think a maester’s life will suit Sam well, and I like the idea of Sam writing all this down at the end. I think Sam will study hard and become one of the smartest maesters of all, but like his new friend Marwyn, he’ll be an outsider and get no real respect.
As for his romance with Gilly. While I don’t think he’ll abandon her, I don’t see it ending with a happily ever after, like in the show. Both Gilly and Sam know in their heads that there is no future together, but they have each other for the moment. It is a star-crossed-romance. Fate will eventually separate them.
Stannis
He’s still alive in the books!
Where we left him in the books: Stannis and his men are preparing to attack Winterfell, they camp on a frozen lake a few miles off Winterfell and seam to be waiting from something. . . The letter Jon gets says that Stannis and his men were defeated, but many fans (myself included) think the letter is a lie.

Where I think he will go: Ramsey is not a long range planner. Ramsey actually does send men outside the castle to fight Stannis, and it’s the men Ramsey doesn’t trust. Ramsey’s plan is to send them to die, but why wouldn’t those northern lords just turn on Ramsey? We know that Stannis is an experienced military commander, and my guess is he’s camped there is trick the brash Ramsey into coming to face him.
I think Stannis will win Winterfell. With winter coming he’ll be snowed in with many northern lords, maybe he will even win over the Northern lords, and be named Rickon’s regent… only to discover that Melisandre killed his daughter. His greatest victory turned to ashes. I see Stannis turning against Melisandre for this. He’ll have a long cold winter think about if it’s worth it to keep fighting for the throne. I don’t think Stannis dies quick and clean. I think he lives with all the pain his wars helped cause.
Cercei
In the novels Cercei has a prophesy that 1) she will outlive all her children and 2) She will be killed by “the little brother” so how will that happen?
Where we left her in the books: Cercei has endured her walk of shame and Quiburn has introduced her to Sir Robert Strong. Most book readers believe Strong to be an undead Gregore Kligan. Cercei is in her uncle’s custody waiting for her trial by combat to try her for crimes of adultery and incest.

Where I think she will go: There are many directions I can see Cercei going at this point, she’s half-mad and very unpredictable, so I’m not sure what she will do. This is complicated by that prophesy about being killed by the little brother. So basically ANY male character might kill Cercei. The Hound, Bran, Jon Snow, Stannis, lots of people are little brothers. Even a face-changed Arya could fulfill the prophecy. but here are three theories that I really like:
- Zombie Tommon. Cercei will stay at King’s Landing, and take control. Somehow Tommon will die, and be resurrected either by Quiburn’s potions or by the White Walkers, and Tommon will kill Cercei. This would have been a poetic ending in the show as Cercei was shown caring so much for her children, but in the book, Cercei sees her kids as chess pieces. While interesting, I don’t see this happening.
- Edmure Tully. Cercei will go back to Castrly Rock after the death of her children. Edmure Tully will escape from his cell in Casterly Rock and seek out Cercei for some revenge about ruining his wedding. So Cercei will be taken out not by some major player, but by someone Cercei only thought of as Catelyn Stark’s little brother. While it is nice twist having Cercei taken out by a minor character, I don’t think so, because the next theory is just poetic.
- Jamie. Jamie has fallen out of love with Cercei in the books, even ignoring her letter about being put on trial by the High Sparrow. In this theory, Cercei will stay in King’s Landing and someone (Young Griff or Danny) will invade putting her trial on the sidelines. Cercei will use the chaos to kill some enemies with wildfire and when Jamie sees her “burning them all” he will kill her to save the city.
Jamie
Where we left him in the books: after learning that Cercei has cheated on him, Jamie is bitter and wondering around the Riverlands feeling sorry for himself. Brianne shows up and convinces him to follow her. Based on an earlier encounter Brianne had in the books, she is leading him to Lady Stoneheart (Catelyn Stark’s reanimated corps) to answer for all his crimes.

Where I think he will go: I think Jamie will be given his life in return for something Lady Stoneheart will demand he do for her (much like Brainne was) I don’t know if that will be something like finding Arya, or killing Cercei. But I think Jamie is going to have some new, well armed, friends following his every move and a VERY clear goal.