Quest stories have always been a part of Western literature. They may not be quite as important as they once were, but they're still to be found all the same.
A great example of a modern-day quest story is Paulo Coelho's The Alchemist, where the protagonist, Santiago, embarks upon an epic quest to find long-buried treasure in Egypt. In the course of his long and eventful journey, he learns a lot about himself, a conventional aspect of the quest, wherever and whenever it takes place. In fact, one could say that what Santiago learns about himself, life, and the universe is ultimately more important than the treasure itself.
Another quest story is "Araby" by James Joyce. Here, the unnamed boy narrator embarks upon a very different kind of quest to that of Santiago in The Alchemist. In a bid to impress a young girl for whom he's fallen in a big way, he endeavors to travel to a bazaar, where he hopes to buy her a nice gift.
On the face of it, the boy's quest may not appear to be in the same league as the legendary journeys embarked upon by Jason in search of the Golden Fleece or Odysseus in his bid to return home to Ithaca after a long exile. But when it comes to a quest, it's not so much the object that matters, but how the individual feels about it. In other words, what unites all the various kinds of quest stories from Homer right through to Joyce and beyond that to Coelho is the essentially subjective nature of the quest, the significance that it has for the individuals concerned.
That's not to say, of course, that the objects of quests are necessarily unimportant themselves. But what matters most of all is the significance they have for the individuals embarking upon the quest. For them, there is always a lot at stake.
This concept is reflected similarly in The Journey to the West. In this work, the object of certain characters' quest is the delivery of Buddha's law to the Chinese people. But also significant is their spiritual development as individuals along the way.