I tend to be like your friend, Cardigan. And I was an English literature major, of all things. I rarely re-read a book. Even my favorite books, Lolita and Master and Margarita, I think I’ve only read twice. I don’t think I’ve read any books more than that. That said, I tend to be the same way with other aspects of culture: I rarely re-watch movies; I almost never replay video games. I do listen to music over and over, though.
I have read the Tolkien books cover to cover so many times over the years I’ve lost count. That includes The Hobbit, The Lord of the Rings, and The Silmarillion.
A somewhat distant second would be the Heinlein juveniles, especially Starship Troopers; I read them a LOT when I was young, and even up to my early 40s. Also a favorite from that genre was Tunnel In the Sky.
Of the books I’ve read since adulthood, the most re-read ones are by Cherryh and Weber.
Oh, I do have to admit that, as a father, I’ve probably read Fox In Sox and Green Eggs and Ham more times than I’d care to admit. Mostly, of course, aloud. 
It’s a ceaseless onslaught…
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I usually opt for something new even though I have reread LOTR about half a dozen times. Lonesome Dove perhaps three times. And I just recently reread the Mars Trilogy by Kim Stanley Robinson. I’ve read some Alistair MacLean’s multiple times but those are incredibly fast reads.
One Flew Over The Cuckoo’s Nest. I love that one. I advise everyone else to check it out, too, if you haven’t. If you read it and don’t like it, well, that can’t be my fault!
Jack Vance’s “The Demon Princes” series, five sci-fi/space opera adventures. Brilliant, some of his very, very best work.
I’ve only read the first three. How are God Emperor and the rest?
Nearly all of Dick Francis novels.
I keep them in a box. Pull them out every few years and reread every book.
I’d estimate every book has been read 6 or more times. The one exception is The Edge. I’ve reread it almost every year since it was published. At least 18 times.
He’s the best mystery writer that ever lived.
His books are a fast read. I get through one in a afternoon.
Shogun
Armor
The Coldfire Trilogy
It
Salem’s Lot
The Dark is Rising books by Susan Cooper
Dracula
The good stuff is really worth reading again and again.
The complete works of Elmore Leonard.
The Chronicles of Narnia (minus The Last Battle), which I reread yearly for almost a decade. And had a second reread in some of those years.
Good night moon, and the very hungry caterpillar.
But for myself? The Lord of the Rings. I read that every year from second grade through high school, and a few times since.
Opinions vary greatly but I really like GEoD, however many people hate it. HoD and CH:D work together and I like them as well.
I don’t reread much, but I used to read the Foundation trilogy every year or so. Not for a couple decades now. I have read LOTR many times, Hobbit only a twice. I read the Harry Potter series a few times, although the last time, stopped after about #4. I recently discovered Sharon Shinn and read her “Blessings” series twice in rapid succession, enjoying it more the second time through since I understand the back story better. I may reread the “12 Kingdoms” series, although it is less compelling.
Then there is Dr. Seuss. I have read most of them countless times, first to my children, then to my grandchildren. No great grandchildren in the offing, but who knows? To a lesser extent, Pooh too.
This… although I sometimes do read The Last Battle because of the part with the soldier who devoted his life to Tash (a different and kind of mean god compared to Aslan) but still made it through the door. Any vestiges of Christianity left in me I owe to C.S Lewis now that I’m about 99% agnostic (kind of hard to shake that evangelical upbringing completely).
I just re-read (or rather listened to) Jane Eyre- a great narration by Thandie Newton and having it read to me was just an outstanding experience. I always come to that novel and see it in a new way and I think now I am finally old enough with enough life experience to fully appreciate it even though I’ve read it at least 10 times previously.
Lastly- Lonesome Dove- an adventure that never loses it’s appeal.
Same here. Pterry’s (sadly) complete works in digital form go with me everywhere.
That was my first one. I re-read it about every four to five years.
Sense & Sensibility. Ten million times.
Lord of the Rings & The Hobbit by Professor Tolkien.
Moon is a Harsh Mistress,** Starship Troopers** by Heinlein.
Then probably the Heinlein juveniles.
I rarely reread a book, as there are just too many unread books out there, and too little time. A couple that do come to mind are The White Nile, by Alan Moorehead, a riveting history of exploration on that river; and The Milagro Beanfield War, by John Nichols, possibly the funniest book I’ve ever read.
The Hitchhikers Guide the the Galaxy followed closely by Life the Universe and Everything and then The Restaurant at the End of the Universe and So Long and Thanks for All the Fish.
There was a period of time between 7th grade and some time in my early college career where I would read them or listen to an audio book, or the BBC radio plays, every single day. I have likely read the first book well over 100 times.