Folklore, Legend and Mythology, Adventure, Epic Poetry, Comedy, Philosophical Literature
OK, so on the most basic level, Ovid's poem is a collection of Folklore, Legends, and Mythology from the Greek and Roman cultures. You can tell this from its focus on gods and demigods and their interactions with humans, as well as Ovid's occasional asides where he tells us things like "or so people say," "hey, I'm just reporting what I heard," and so on.
That said, because myths are an attempt to understand the world, they can be about just about anything, so Ovid's poem branches off into all sorts of other directions too. Sometimes, different genres can be blended together. For example, in the battle between the Lapiths and the Centaurs, from Book 12, Ovid borrows the presentation format from epic poetry: long lists of who-killed-whom in exhaustive, gruesome detail. At the same time, however, it is clear that Ovid is making fun of the genre, so that this passage can also be interpreted as an especially violent form of slapstick comedy. There are also various passages in the poem that could be thought of as part of the adventure genre – think of the tragic expedition of Daedalus and his son Icarus, or the travels of Aeneas recounted in Books 14 and 15. Finally, because Ovid tries to create a philosophical basis for his poem in the long speech of Pythagoras in Book 15, his work also counts as philosophical literature.