Several major and minor houses were destroyed during the 8 seasons of Game of Thrones. The Boltons are gone. So are the Tyrells. Are all of the Mormonts dead? And the Umbers too?
Which major and minor families were destroyed?
By destroyed, I mean that all known members of the family are dead - not just that the family was unseated from their holdings. (You could say that the Targaryen family still exists while Jon Snow still stands.)
Mike Scott makes a good point that cadet branches, branches along a female line, and women married to other families might still be part of the family.
For families that follow only the male line, if a woman marries into another family, her children have claims to her husband's holdings, not to her father's holdings.
Cadet branches are the lines of a male ruler's younger sons, and they still have a claim to the family holdings. If a cadet branch exists, then it counts.
Illegitimate children have no claim to their parents' titles and lands in Westerosi tradition, so they and their children don't count for this question.