I think some of the most popular books about a quest are the Percy Jackson series. I have never read them, but have seen parts of the first movie. It looks somewhat entertaining and is on my list of books to eventually read. Percy is a demigod whose father is Poseidon. His various quests are to save his friends and the gods of Mount Olympus.
Harry Potter ends up being a sort of a quest, at least in Deathly Hallows. He is on a quest to find all of the Horcruxes and to defeat Voldemort once and for all.
Then you have the Warriors series and by the same group of authors the new Seekers series. Warriors is about a group of cats that live in the woods in different clans and are sent on various missions. Seekers seems to be a similar concept, only involving bears.
Numerous other series exist and new ones pop up on my freebies list for Kindle every day. What are some of your favorites?