Fantasy, Quest, Coming-of-Age
It's hard to miss that The Hobbit is a fantasy novel, what with all of the elves and goblins and trolls and things. And The Hobbit is also clearly a quest because the whole engine of the book is Thorin and the dwarves' plan to seek their stolen gold in the lair of the dragon Smaug. Finally, this also counts as a coming-of-age story because it depicts the development of Bilbo Baggins from a sheltered, comfortable homebody to a brave, wise hobbit of the world.