The Freys and Boltons are definitely screwed but I didn't include them in the list because they're not one of the major houses, even though Tywin made Roose the Warden of the North and the Freys to run the Riverlands; neither deal will be permanent.
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.
Not sure how I feel about Sansa and Tyrion staying together/conflicted about it. On one hand, I could see them deciding to stay married, consummate it and have children; on the the other hand, I feel like they'd mutually agree to annul their marriage.
I definitely consider Rickon and Trystane to be the ones to continue the Stark and Martell lines and that is their main significance for being in the series.
I could see Roslin's son living and inheriting Riverrun, but I'm not sure about Edmure surviving. Could go either way. Hence the reason why I included the Tully's in my list of possibly going extinct, although they probably won't; the Starks, Martells, and Tyrells for instance have a lot more live folk hanging around than the Tully's.
I think the Greyjoy most likely to live is Asha. Asha doesn't seem like the type to settle down and resume a traditional Westeros female role but if she wants the line to live then she needs to marry a man, have him somehow take the Greyjoy last name, and have children. Otherwise, they're done.
I think Tyrells stick around mainly because there's so many of them.
Arryns are definitely done and I don't even know if Sweetrobin could have the strength or 'vitality' to produce heirs.
Baratheons are dunzo unless one of Robert's bastards is legitimized, but I'm not sure if that will happen.