-Targaryen ( [F]Aegon is not real and Dany will probably die towards end of series)
Dany won't have children and it would be very difficult to prove Aegon's birthrights.
Now that Sansa sees Baelish for what he is and is starting to see how unfair the world is, I see Tyrion actually rescuing her and their marriage continuing with children.
This one rests with Rickon now. I see Rickon being the strongest of all the Starks in the end and I think Bran helping to look out for him through the network. The reason why I say Rickon will be the strongest is because he won't be raised with the naivety of Ned and Robb, he will be colder and more business like.
The Martell's will have their family cut down a lot when they enter the war with Aegon coming over. We will see how much of their line continues.
Tyrell's are coward enough to aid whoever is winning so i can see them surviving.
Baratheon is all but done. Stannis won't have another heir, he will die like a boss but won't have another heir. The only chance that the Baratheons have is for Brienne to bring Gendry to Stannis and he gives him the Baratheon name when seeing so much of his brothers in him.
Arryn is gone.
For some reason I see Edmure surviving and keeping the Tullys around. I think Roslin has a son to keep the name around.
Greyjoys will stay around too. They are survivers. Not sure who will keep it going but they will.
The family I am most interested in is the Freys. I see them sticking around but it would be amazing reading to see them all being hunted down.