Time travel novels seem to travel between genres: you can find them in Mainstream, Literary, Sci-Fi, Mystery, Romance, and Women's Fiction. Between H.G. Wells' The Time Machine and Diana Gabaldon's Outlander series lies a vast continent of uncategorizable stories involving moving backwards and forwards in time.
Having just written a time-travel novel, The Renaissance Club, involving a young art historian and her artist-hero, the great Italian sculptor Gianlorenzo Bernini, I've been reading stories that hinge on magical treatments of time. I like to call them time-bending stories.
Here's one of my favorite time-travel novel lists, from LibraryThing. I love that it encompasses the spectrum of treatments, from Poul Anderson's and Ray Bradbury's serious considerations of time-travel mechanics and consequences to humorous uses of device, as in Douglas Adams' books. However, the omission of Kate Atkinson's intriguing Groundhog Day style novel, Life After Life, is a serious one. I think alternate reincarnations and versions of the same life should count as time travel.
And that's the beauty of the device: its infinite possibilities. In my novel, I have a time-traveller going back to alter a single moment in time and thus erase one masterpiece, changing the history of art. I don't much enjoy thinking about quantum physics and its relation to time travel, but I really enjoy the idea that history (time) branches off into infinite possibilities. Maybe those alternate worlds are contained in those baby universes posited by Stephen Hawking, the ones that might even at this moment be passing through your body.