Some of us are so forgetful that it is not uncommon to forget what books we have read.
I sometimes forget that I’ve reread a book before.
Until I actually start reading. Usually I realize the plot is oddly familiar within a few pages.
I often don’t remember all the details. It’s fun rereading a book and rediscovering why I enjoyed it the first time.
The Cruel Sea. Some of the descriptions almost make you queasy with seasickness. The same way that Jack London’s To build a Fire makes me feel cold.
Foundation Trilogy, Rendevous with Rama (and Rama 2, etc.).
Guy Murchie’s Song of the Sky and Music of the Spheres.
Canticle for Leibowitz.
Fiction
The Wizard of Oz by L. Frank Baum (when I was a child)
Mrs Frisby and The Rats of NIMH by Robert C O’Brien (when I was a child)
Replay by Ken Grimwood
Jumper by Stephen Gould
*The Man Who Folded Himself *by David Gerrold
Nonfiction
Guns, Germs, and Steel by Jared Diamond
*One Child * by Torey Hayden
The Late Shift by Bill Carter
The War for Late Night by Bill Carter
Book about the Paranomal (they maybe nonfiction. they maybe fiction)
Time Storms by Jenny Randles
Alien Agenda by Jim Marrs
The Gods of Eden by William Bramley
Borderlands by Mike Dash
Swallows and Amazons (Ransome).
Tarzan of the Apes (Burroughs).
Metzger’s Dog (Perry).
The Princess Bride is on my reading list (never read.)
My contributions are Alice’s Adventures in Wonderland & Through the Looking Glass, which I have read at least as many times as I’ve had years. I now own an annotated version which gives historical and cultural context to every little detail. Then there’s Catcher in the Rye, which I know to be very polarizing but I personally find both hilarious and poignant. I also re-read whatever I can get my hands on by Ray Bradbury, and love Stephen King’s short stories. Then there are my comic book collections: Calvin n’ Hobbes, Foxtrot, the Far Side… I’ve read all of that a million times.
I’m not a huge re-reader, TBH. There are too many shiny new things.
The Lady and her Tiger by Pat Derby. Her autobiography telling tales of her many wonderful animals. Read it so many times I can recite parts from memory.
The Girl Who Loved Tom Gordon by Stephen King. My favorite of his writing, delightfully creepy
Bluegrass by Borden Deal. Wonderful story about horse racing
I have two huge volumes of Maugham’s short stories, remarkably entertaining. Mostly centered around the Brits mixing it up with the natives at the turn of the century in hot places, like Malaysia, Viet Nam, Hawaii. (There are some great short stories about a spy named Ashenden, and I swore they were the basis for James Bond, but these were set in WWI!). If you’ve ever seen ‘Red Dust’ with Clark Gable, Mary Astor, and Jean Harlow, this is just what I’m talking about.
I’ve read Gary Jennings’s historical epic Aztec four times, I think, and George R.R. Martin’s environmental sf satire Tuf Voyaging at least that often. They’re my all-time favorite books. I don’t think I’ve read any other book more than three times.
I just re-read this the other day. It’s up there with some of my favorites by Stephen King. Now I want to re-read The Eyes of the Dragon, that’s another of my favorites.
I’ve re-read the Lord of the Rings trilogy many times. I keep meaning to attempt to re-read The Silmarillion to see if I can get any more out of it upon a second read-through.
I’ve probably re-read my Chronicles of Narnia set the most. I still have the set my aunt gave me when I was 8, I probably read through them once a year or so. I think my oldest niece will get a set of the books soon, she’s 8 now herself and I think she’d enjoy them as much as I do.
I re-read books pretty frequently, often due to circumstances limiting accessibility of new material (bathrooms, planes, at my desk while scripts are running in the background) and having a deep trove of ebooks on my phone that allows me to easily access past reads.
I also re-read a ton of books when I was younger, due to not having money or as many trips to the library as I’d have liked. So for me at least, there’s a pretty long tail of “I’ve re-read this 2ish times” books. But the books that have made the cut above that threshold that immediately occur to me are:
Kinda Philosophical:
Robert Pirsig’s Zen and the Art of Motorcycle Maintenance
Herman Hesse’s Siddhartha
Gregory David Roberts’ Shantaram
Neal Stephenson’s Anathem
Sci-Fi:
Peter Hamilton’s Judas Unchained and Pandora’s Star
The first three books in Orson Scott Card’s Ender however-many-there-are-nowlogy, Ender’s Game, Speaker for the Dead, and Children of the Mind
Nancy Kress’ Beggars in Spain
Frank Herbert’s Dune, God Emperor of Dune, Children of Dune
Pretty much everything by Neal Stephenson, but Cryptonomicon particularly
Charles Stross’ Accelerando
Verner Vinge’s A Fire Upon the Deep and A Deepness in the Sky
Other Fiction:
Norman Rush’s Mating
David Foster Wallace’s Infinite Jest
James Clavell’s Shogun
Mark Danielewski’s House of Leaves
Tolstoy’s Anna Karenina
Dostoyevski’s Brothers Karamazov
Non-Fiction:
Jared Diamond’s Guns Germs and Steel
Dubner and Levitt’s Freakonomics and follow ups
John Allen Paulos’ A Mathematician Reads the Newspaper
Dan Ariely’s Predictably Irrational
Nicholas Nassim Taleb’s The Black Swan and Fooled by Randomness
Thaler and Sunstein’s Nudge
Needless to say, I would and do heartily recommend these to friends and family, and unreservedly recommend them to anyone here in the same spirit. 
I don’t like to reread books, because it takes time away from reading one I haven’t read. My reading time is limited. But I think I read The Magic Journey twice, John Nichols’ second installment in his New Mexico trilogy of which The Milagro Beanfield War was the first. I think I read some of the Tony Hillerman mysteries twice.
I read rather quickly and thus go through many of them. I often find myself without a new book to read without a trip to the library, and thus must re-read. We probably have a thousand books in the house; I’ve never tried to count them.
The ones I most often re-read are:
Earth Abides
Harry Potter (all of them)
The Godfather
Anything by Asimov
Ender’s Game
Speaker for the Dead
Lots of nonfiction, especially anthropology, evolution and medical history.