Lots of the great house of Westeros are in a state of chaos.
HOUSE STARK - Three legitimate heirs: Bran (first in line, but paralyzed), Sansa & Arya. Bran is currently MIA to the rest of the family, making the situation more murky. Jon Snow is considered part of House Stark, but is currently regarded as a bastard. At least until the rightful Lord or Lady of that house, or the King, legitimizes him. And of course, he is more likely a claimant to House Targaryen, but nobody really knows that on the show except for Bran.
HOUSE ARRYN - The only heir at this time is Lord Robyn Arryn, and that boy is clearly quite troubled. And we haven't seen any other Arryns ready to step into his place. Will Petyr Baelish step in to become the Lord of the Vale should something happen to young Lord Robyn?
HOUSE LANNISTER - Three heirs to be the Lord or Lady of Casterly Rock: Jaime Lannister, Cersei Lannister and Tyrion Lannister. Tywin had disowned Jaime for remaining with the Kingsguard prior to his death. And Kevan had distanced himself from Cersei. Tyrion is regarded as a kinslayer for having killed his father, Tywin. And now that Cersei's children, Kevan and Lancel Lannister are all dead, who is left? In light of Cersei's coup d'état for the Iron Throne and Jaime having been dismissed from the Kingsguard, I suspect that he will become the Lord of Casterly Rock despite Tywin's proclamation. And does Jaime potentially get with Brienne of Tarth? That storyline has bubbled under the surface. Unless of course some lesser Lannister rises up.
HOUSE TYRELL - Following the events of the Green Trial, only Lady Olenna is left alive. Mace? Dead. Margaery? Dead? Loras? Dead. The Queen of Thorns is the only other Tyrell that we've seen on screen. We never saw either Willis or Garlan Tyrell on the tv series.
HOUSE MARTELL - Between Oberyn's fight with the Mountain, and the treachery of the Sand Snakes having killed Prince Doran and Trystane Martell, there doesn't appear to be a true born Martell left to rule Dorne. While the Dornish are much less judgemental about bastards, can they have a Sand rule Dorne?
HOUSE BARATHEON - No true born Baratheons remain: Robert is dead, Renly is dead, Stannis and his family are dead. Robert's bastard children were almost entirely eliminated except for Gendry. And the children Robert believed to be his are all dead as well. It seems that House Baratheon may be dead unless the monarch upon the Iron Throne recognizes Gendry and he is allowed to rebuild this house. And you know that Cersei isn't going to do that.
HOUSE TARGARYEN - Danaerys lives, but the only child she bore was stillborn thanks to the Lazareen witch's magic. Jon Snow seems likely to be a Targaryen as the son of Rhaegar, but has not been recognized as such.
As for some of the lesser houses?
HOUSE FREY - Thankfully, the late Lord Frey is finally LATE. Thanks, Arya. She also took out Black Walder and Lothar Frey in the process. But there are lots of other Freys, and I suspect that they're going to be at each others throats for power over the Twins.
HOUSE TULLY - Riverrun is lost to the Freys and the Lannisters. The Blackfish is dead. And Lord Edmure was a captive of the Freys. Will Arya have freed Edmure in the process of taking out Walder Frey? Will the Tullys have any sort of future?
HOUSE GREYJOY - Euron Greyjoy reigns the Iron Islands. It's not clear if Aeron and Victarion are in the mix as well. Yara doesn't seem prepared to marry and Theon lost his favorite toy. It's certainly complicated.
Danaerys has spoken of breaking the wheel of Westeros. It looks like the infighting among the great houses has done most of that for her already!