Ursula K. Le Guin: The Left Hand of Darkness
Robert Charles Wilson: Darwinia
Joseph Conrad: Heart of Darkness
Charles Wright: China Trace (poetry)
קֹהֶלֶת (Ecclesiastes)
Stephen King - “The Stand”
Harry Turtledove’s Southern Victory series, all eleven books. (I’m currently re-reading book nine right now).
The Lord of the Rings is probably first on my list and it’s probably the only one known to a wide audience.
I really enjoy Peter Watts’ work, and I’ve read through each of his novels a few times. They’re hard sci-fi with a lot of real science to them (including a list of references after each book).
Even better, it’s a dark, dystopian future filled with screwed up people, and the writing is done in a way that almost compels me to keep reading. My other favorites also share that:
Becoming Human by Valerie Freireich.
Armor, by John Steakley.
Discworld novels and Patrick O’Brian’s sea stories, read them over and over .
Me too; so it goes!
Mercedes Lackey’s novels of Valdemar–The Mage Wars, Last Herald Mage, Collegium Chronicles, Vows & Honor, Kerowyn’s Tale, Heralds of Valdemar, Mage Winds, Mage Storms, Owl Mage trilogy.
Lots of them. A few that aren’t on the other lists:
The Shadow of the Shadow by Paco Ignacio Taibo II. Four friends meet for dominoes in the bar of the Metropolitan Hotel–Mexico City 1922. They fought in the Revolution & cynically watch a new order suspiciously like the old order beginning around them. Then they begin investigating a couple of suspiciously linked murders. Taibo has political axes to grind (with which I generally agree) but the atmosphere & characters are what keep drawing me back. Need to try it in the original Spanish.
To Say Nothing of the Dog by Connie Willis. Time travel, high Victorian wit and a bit of her favorite Blitz. Whenever I need to smile…
The List of Seven by Mark Frost. Young A C Doyle visits a seance; he’s writing on the occult to fill the spare time left by his medical practice. Shocking occurrences lead to amazing adventures across Britain with a brilliant, mysterious agent who will inspire his future writing. A truly ripping yarn.
Parade’s End by Ford Madox Ford. Four novels dealing with a very bad marriage & the Great War. Ford’s modernism isn’t as difficult as his friend Joyce’s version–but the story isn’t told in a linear fashion. Beautiful writing & unexpected humor are the carrots on the stick that keep the reader going. Then bring the reader back.
Jane Austen, umpteen times (Sense & Sensibility, Persuasion, Emma and Pride & Prejudice)
Mark Heprin, Winter’s Tale and Soldier of the Great War
Lord of the Rings
The Haunting of Hill House
Bleak House
Mrs. Dalloway
Rebecca
Goodbye Darkness - William Manchester
Most of mine have already been mentioned- but when I’m having a really bad day, nothing quite beats a re-read of any of the Little House on the Prairie books. A simpler world in many ways 
The Lord of the Rings
anything by Georgette Heyer
anything by PG Wodehouse
The Wind in the Willows
Winnie the Pooh and The House at Pooh Corner
Bailey White’s Mama Makes Up Her Mind
I think I am the second one in this thread to mention the Maturin-Aubrey series of 21 books from Patrick O’Brian. I have read the entire series 4 times so far.
All the discworld books
1984
Lovecraft: at the mountains of madness, call of cthulu, shadow over innsmouth
LOTR trilogy
The hobbit
Hitchhikers guide
An old elizabeth cadell book called a lion in the way
Gosh…
Harry Potter series. Primarily books 1-4. Particularly book 3. I’m rather fond of Lupin and Sirius. Strongly dislike Lupin’s look in the movies (he looks like a child molester, IMHO).
Good Omens. Sometimes when I just don’t know WHAT to read I’ll pick it up again.
Kamikaze Girls by Novala Takemoto and Masumi Washington. Goofy damn book with an overall positive message (friendship is awesome!)
The Stand by Stephen King or The Talisman by King and Peter Straub. I must be a masochist.
Travis McGee (John D. MacDonald), Nero Wolfe (Rex Stout), and Wallander (Henning Mankell) are my big 3.
I’m not a subscriber to the “why do you need to read it more than once” school of thought. If I like a book it gets re-read at least a few times. There are some books/series that I re-read at least every couple of years. These include:
the Hitchhiker’s Guide to the Galaxy series, the Dirk Gently books (to me the Long Dark Tea-Time of the Soul is at least the equal of Hitchhikers), and Last Chance to See (which is almost criminally under-rated).
Lord of the Rings, the Hobbit, the Silmarillion, Unfinished Tales, and the Children of Hurin has been added to the list since I picked it up last year. It’s a shame the Tale of Beren and Luthien was never finished, it would have been an awesome story to read in full.
the Discworld series
Weaveworld (Clive Barker) this is one of my favorite books of all time. There was once a mini-series planned, I’m not sure if I’m happy or sad that it fell through. I can hear and see every scene, character, and line of dialogue in my head, to put it on film might ruin that.
The Great Gatsby - I know a lot of people that have read this, no one else who actually liked it. I thought it was fascinating (although tragic).
To Kill a Mockingbird - Just really well written and an amazing book.
Eyes of the Dragon - I started to intensely dislike Stephen King’s writing style at some point in the past and can’t re-read too many of his books now, but this one’s still a favorite.
Another Day, Another Dungeon and One Quest, Hold the Dragons - I am upset that the author never finished the series, it was kind of a parody of fantasy but very well written and funny IMO. A favorite since I discovered it in the mid 80’s.
I forgot about a lot of these books mentioned, which I HAVE read many times, like Winnie the Pooh, The Stand, The Haunting of Hill House.
I will add: Forever Amber, Strangers In The Forest, Green Darkness, and Katherine (both historical novels by Anya Seton), National Velvet, and Little Women! (I must have read Little Women a million times.) Onions In The Stew, by Betty McDonald, non-fiction, about living on Puget Sound during WWII (movie: The Egg and I with Claudette Colbert, in the 40’s).
And any of the All Creatures Great and Small books. (I must have read all of Herriott’s books two million times.)
No one else who liked Gatsby? Huh. Well, count me as one.
Stephen King The Stand (and I always seem to get a cold 3 chapters in to it - either my paperback is crawling with germs, or I’m extraordinarily suggestible. Little from column A, little from column B)
Ken Grimwood Replay , my absolutely favourite book of all time, by a country mile. I’ve been enchanted by it since the first time I read it, 20+ years ago, and I read it at least annually.
Generally I’m a re-reader, but those two are by deliberate choice, rather than “umm nothing to read, may as well go with this again”.
There are a lot of books that I did read obsessively at one point, but not currently doing so and may never touch them again. However, that list would be pretty long so I just kept it to books that I’ve been re-reading over the past 2-3 years.
I would include the Turtledove Civil War alternate history (starting with “How Few Remain”) series in that list, btw.