Keep in mind, these decisions are based primarily on the HBO show, not on the book series.
WARNING: Spoilers for HBO’s Game of Thrones ahead.
Gryffindor - Bravery, daring, nerve, chivalry
It is often said of Jaime that he is brave to the point of stupidity. He will gladly charge into battle because it is one of the only places he feels truly alive, and because he is quite good at it. In fact, other than being a Lannister, he is known for exactly two things: bravery, and being an oathbreaker.
Arya is also brave to the point of being stupid. She puts her life on the line even when it doesn’t really help anyone because she feels that she has something to prove. She wants to fight and to get revenge for her family, but more than anything else she wants to never feel helpless again.
Robb takes after his father in a number of ways, but he does not value loyalty or fair play as much as Ned. Robb betrays his promise to Walder Frey, which Ned would never have done. It is clear that Robb is a bit more selfish than his father, but no less courageous.
Robert winning his war can be attributed in no small part to his fearlessness. He inspired loyalty and respect in his soldiers by charging into the heart of battle right alongside them, something that also struck fear into his enemies.
Brienne of Tarth
Brienne is a cut-and-dry Gryffindor. She is courageous in battle, willing to put her life at risk for others, and she has to stand up and be brave in the face of a society that thinks there is something wrong with her because she wanted to become a knight instead of a wife.
Drogo is leader of a group of ruthless soldiers who only respect strength. He has to continually prove himself daring just to keep from being killed or having his followers leave to start their own Khalisar. Drogo is also willing to face that which his people fear most, the sea, in order to give Daenerys what she wants.
The Red Viper is willing to brave the halls of the most dangerous place in Westeros and face off against the deadliest political players to get revenge for his sister’s murder. He doesn’t hesitate to volunteer to fight The Mountain if it means killing the man who terrorized his sister and her children.
The Lord Commander of the Night’s Watch has to be able to command the respect of a wide array of men, so he can’t rely solely on his noble blood as he might have done anywhere else in Westeros. Instead, he commands respect by proving to his men that he is as capable and bold a soldier as they are.
Hufflepuff - hard work, patience, loyalty, fair play
Well, he can’t be a Ravenclaw because he knows nothing. Jon Snow is defined by his loyalty: loyalty to his family, to his Oath, and to his Brothers. Even when he seems to turncoat and join the Wildlings, he is only doing it because it is the best way to protect the other men of the Night’s Watch.
Ned Stark is the most honorable man in Westeros. He values fairness and justice above all else, certainly above courage and valor. He passes up most opportunities for greatness because he does not want the limelight – he only wants to be a fair ruler to the people of the North.
As a smuggler, The Onion Knight might not seem like a good candidate for Hufflepuff, but Davos has shown himself to be Stannis’ most loyal attendant. He does not leave Stannis’ side when they disagree, or when he thinks Melisandre’s hold has grown too strong. Davos continues to try to support Stannis and make him see reason, even when imprisoned in a dungeon.
Ser Jorah’s loyalty to Daenerys has hardly wavered since the moment he met her, and he is certainly the most tempered of her advisors. He always encourages her to be fair and patient, but at the end of the day, he would do anything she asked of him.
The only thing Theon really wants is a place where he belongs, and that is something Hufflepuff will offer anyone who desires it. He feels abandoned by the Greyjoys and rejected by the Starks, and is easily broken by Ramsay Snow because he feels he has nothing to fight for. Given a home where he feels accepted and respected, Theon would likely be loyal and happy.
What is Catelyn, if not loyal to her family? She would do anything for them, particularly Ned and Robb. She set Jaime free, a man who tried to kill her son, because she thought it might bring her daughters back to her. In this, she is not unlike Cersei. The difference is that Catelyn is not interested in power or manipulation.
Everything Stannis does, he does because he thinks he is King by rights. If he felt he had no true claim, he would not pursue the Iron Throne. He feels robbed of what is rightfully his, which is not fair or just, and fairness is very much Stannis’ game.
While the Hound isn’t defined by any particularly Hufflepuff-esque traits, he also doesn’t fit especially well into any of the other houses. He isn’t particularly brave or chivalrous, he doesn’t value intelligence, and he has no ambition to speak of. The reason he is in Hufflepuff is, quite simply, because Hufflepuff is the only house that would take him.
Ravenclaw - Intelligence, curiosity, wit, creativity
Tyrion professes more than once that he derives all of his power from knowing more than his competition. He reads often and makes sure to keep company with other knowledgeable people, like Varys. He recognizes that his strength is not charisma, manipulation, brawn, or bravery, but only intelligence.
Varys “the Spider” is Master of Whispers, and therefore deals almost entirely in intelligence and information. Of course, he is capable of manipulation and he is ambitious, but he is ambitious only insofar as it serves the realm. He has made it his business to know everything about everyone, often before they know it themselves.
Tywin is a very smart man, and he wins wars not by being stronger or more honorable, but by knowing more about his enemy, the terrain, and the logistics of a battle. He is a brilliant strategist, which he uses in both war and politics.
Sam does put a lot of value in strength and bravery, but that is partially due to his own lack of self-confidence. As he grows more confident, he begins to see that the traits he possesses, like intelligence and curiosity, are just as important as valor.
With age comes wisdom, but I suspect The Queen of Thorns always had a few tricks up her sleeve. She and Tywin aren’t all that different; she keeps her family growing strong by knowing all there is to know about the politics of Westeros, in particular King’s Landing.
Melisandre might not seem like a Ravenclaw at first glance, but that is because she values a non-traditional sort of knowledge. What she finds important is the knowledge that the Red God imparts. As a seer, she know things that no one else knows, and though she finds power in it, it is not for the sake of power that she does it. Melisandre truly believes in the Lord of Light.
Bran Stark is somewhat like Melisandre in that he gains his knowledge from a nontraditional source. He sees things that no one else sees through his abilities as a Warg. He trusts in his supernatural abilities, and those of Jojen Reed, believing that he knows something no one else does. He also knows that he must deal with this himself, as no one else is likely to believe him.
Jojen has greensight, a power that allows him to have visions of things he shouldn’t rightly see. Naturally, he understands that this gives him a unique insight into the world, and that he ought to use the information these visions give him for the good of the realm. Clearly he finds the knowledge from these visions very important, because he convinces Bran to accompany him on an impossible quest because of it.
Slytherin - Ambition, cunning, resourcefulness
Aside from the obvious dragon/snake connection, Daenerys is primarily motivated by her desire for power. She wants to rule Westeros, and she is willing to do nearly anything to achieve that goal. She uses all of the resources available to her, and is not afraid to trick or manipulate people, when necessary, to get what she wants.
Margaery knows how to play the game, and she plays it well. She wraps first Joffrey, and then Tommen, around her little finger with ease, playing to their weaknesses to get in their good graces. She is cunning and capable enough to stand toe-to-toe with Cersei and present a formidable threat to Cersei’s power.
Slytherin doesn’t equate to evil, but a disproportionately large number are predisposed to it. Joffrey is just such a character. A distinct Slytherin trait is pride, and that is something Joffrey has in spades. He is King, and what he says goes. He abuses his power at every turn because he does not believe it can be taken away from him.
Pride does run in the Lannister family, though Cersei is far more clever and cunning than Joffrey. Ultimately, all Cersei cares about is her family. The only thing she wants is their security and happiness, and she is willing to go to any lengths to secure it, including murder. She also believes that keeping the Lannisters in power is the only way to ensure their safety.
Littlefinger is defined by his ambition. It is said that he would watch all of Westeros burn if it meant he could rule over the ashes. He is quite possibly the most resourceful man in Westeros, able to cripple the country and prepare it for his takeover without anyone even noticing.
Many attribute Sansa’s inaction as passiveness or stupidity, but Sansa is actually a very intelligent young woman. She knows that to act rashly would only make an already terrible situation even worse, so she waits for the right opportunity to make her move. As her interactions with Baelish suggest, she is far more capable than she is letting on, because she knows that it is to her advantage for people to underestimate her.
Osha is constantly put in positions where she must use her guile and cunning to survive. She has to play the loyal servant to the Starks so they won’t kill her like they did her companions, and when Theon takes over Winterfell, she tricks him so she can help Bran and Rickon escape. She uses whatever resources she has available to help her survive.
For a woman in Shae’s position, resourcefulness is a necessity. She is highly adaptable, and looks out for herself before anyone else. She knows that she is capable, which is why she doesn’t want to run away from the dangers posed by Tyrion’s family, even though she doesn’t understand how much danger she is really in.