Lord of the Rings is quest literature at its best. A quest is what happens when a character (or characters) travel to a far off destination with the sole purpose of achieving some goal. Clearly, Frodo's journey, first to Rivendell and then to Mordor to figure out what to do with the Ring of Power, fits that definition nicely.
It's not tough to see why Fellowship is an adventure, either. If it were easy for Frodo and his friends to travel in the direction of Mordor, we wouldn't care much about his Ring quest to begin with. But along the way, they meet their fair share of evil trees, cave trolls, swarming Orcs, and powerful blizzards. These adventures keep the narrative interesting – otherwise, it's just the story of a very long hike.