Hadn't thought about this in a very long time, so I'm not sure how accurate my list would be; but it depends also on what you consider "non-genre". Would Shakespeare's "The Tempest" count? After all, it is fantasy, really, as are "Macbeth" or "Hamlet" -- each of which I've read several times (along with other of his plays and quite a few of his sonnets).
How about Spenser's The Faerie Queene? Again, fantasy (of a sort), and I've read it through three times, with several dips into portions of it over the years... and then there's The Shepheardes Calendar -- ditto. Dante's Commedia Divina -- twice, with an intention to read it at least a few times again. Several of Cabell's books don't actually fit as "genre" save by association, such as Beyond Life, which I've read at least eight or nine times; other of his books at least two or three. Heck, I've read the Malleus Maleficarum all the way through twice... though I suppose few besides myself would consider that fiction -- though, given the history of the thing, and the dubious reception it had even from the Church......
I've read all of Ann Radcliffe's novels at least once, and all but Gaston de Blondeville two or three times; The Romance of the Forest four; The Castles of Athlin and Dunbayne five (though this was more by way of its availability at the time, and its brevity; still, I do like this one....). And, again, I have every intention of reading The Mysteries of Udolpho at least a couple of times again, being very fond of that one as well....
And I've read all of Poe several times over, both fiction and verse; again, I have a fondness for some of his sketches and nature studies, and even for some of his comic pieces (which makes me something of an oddball, I understand....) And no little of Washington Irving, for the matter of that....
I, too, have read most of the Holmesian canon at least two or three times since I first picked them up at age 12; not to mention other pieces by Doyle, of various sorts. And there's multiple readings of a lot of Hawthorne in there, too; not only his fantastic pieces, but a rather large selection of his tales and sketches....
Though it has been many, many years now, I have read The Secret Garden through at least four or five times... perhaps that one deserves a revisit again, too. And then there's Terhune's Lad: A Dog, which was a favorite of mine during my youth. And Joyce's Ulysses twice (never have got around to Finnegan's Wake, though I keep intending to). Loved it both times, once I got over my initial trepidation at tackling this supposedly "difficult" book... a reputation it really doesn't deserve; I found it a delight. (Again, though, given certain points of that one, I'm not sure it doesn't at least tangentially fit as "genre"....)
Then there are "non-genre" pieces by genre writers, such as Moorcock's The Brothel in Rosenstrasse (a personal favorite), and several of his essays; or Ellison's stories of juvies or his screenplays (sff and otherwise), essays, suspense or crime tales, etc.; all of which I've read more times than I can even remember. Ditto Bradbury's The Anthem Sprinters and other of his non-fantastic plays; or non-fantastic stories, for the matter of that. (I suppose I should leave out the essays, and perhaps the plays, but as I'm doing this off the cuff....) Some of Asimov's mysteries I read more than once when young, such as A Whiff of Death. And Ethel Lina White's Wax I read until the darned thing fell apart on me.... Various of Maurice Level's contes cruel over the years; and I'll probably revisit his Tales of Mystery and Horror (the single collection of his tales I own) once or twice again as, like Maupassant, they are fine exemplars of the short tale. And more of the latter writer's works than I can remember at this point -- a true master craftsman. A few (less than I'd like) of Balzac's works, such as the oft-reprinted "Le Grande Bretèche" and some of his Contes Drolatique....
