I have a few quest stories, for example.
Epic Fantasy - The obvious one. Yes, the epic fantasy involves a quest of some type. The group is on a quest to fight back against a ruler who is trying to overtake every group one at a time. They also end up with different quests over the years as they battle on to reach the end goal. But they aren't questing after a magic object or anything like that, though Feyn does go on his own quest to save the other elf.
Romance - Romance stories can have quests though they may not be physical quests of traveling long distances (though yeah, some have to travel long distances and through time at times). Most of the romance stories I'm writing (whether it's Thomas/Kyle, the rancher with the city boy, the truck driver and femme boy, or anything else) there is a personal quest.
Young Adult - The young adult quest so far is also personal. Ottohahn is on a quest to fit in the place he calls home. Sage is trying to find a place to call home where he can stay. Ephram's quest is to not be a tattle anymore.
I have another one that involves travel quest but it's a sekrit.
Do you use the quest?
What's your favorite quest story?