Another vote for the Bible, and I also had a book of Aristotle’s philosophy (in translation) that I got about 1 page into before giving up.
EDIT: I also didn’t finish Gravity’s Rainbow.
When I was a kid I had friends who were adamant that Stephen Donaldson was the best writer evar. I tried reading Lord Foul’s Bane a couple of times, but didn’t make it past a few chapters. A couple of years ago I gave it another shot - thinking perhaps in the ~20 years that had gone by, maybe I’d matured enough to handle Donaldson or something. I made it about a third of the way through the book. It was just as stupid as I’d remembered.
I’ve read the original two trilogies all the way through several times. 
Mine is Stephen King’s Gerald’s Game. I picked it up because, well handcuffs on a bed, I thought it might be interesting. I get insanely bored about about the 100th page of ‘the wind blew through the grass’ or some such.
Another was a Peter Straub novel that I can’t recall, probably one he co-wrote with King. Maybe the problem is I just don’t like Stephen King’s writing.
The Hunchback of Notre Dame. Victor Hugo couldn’t let a character walk down a street without describing every building on the street in every irrelevant detail. I only made it through Les Miserables because I was crazy about the musical.
Heart of Darkness. It just didn’t grab me. I tried.
Catch-22. I enjoy this book every time I try to read it. The problem has been that I have to top for one reason or another and pick it up again later. There are too many characters and weird situations for me to keep straight if I don’t read it all the way through at once, so I keep starting over.
I have been reading James Joyce’s Finnegans Wake periodically for a couple of decades. So far the furthest I’ve made it is about two-thirds through. Now that I have a family I despair of ever actually making it to the beginning again.
Don Quixote. I make it to about the same point every single time I try. And what’s odd is that 90% of the stuff I’ve ever heard about happens in those early parts so I assume most people don’t make it much further along than I do.
Midnight’s Children. I carried it across two continents and got within 10 pages of finishing it, and then forgot it on a bus in Chile. I’ll probably never pick it up again. When you are traveling you are absolutely desperate for reading material.
War and Peace. Started it a half dozen times, never finished it.
Gravity’s Rainbow. Every time I try to read that I end up half-falling asleep and hallucinate nightmarish scenarios.
No joke, that book is like the videotape from “The Ring” for me.
Here’s a recent one: “And Another Thing…,” by Eoin Colfer in the reboot of “The Hitchhiker’s Guide to the Galaxy” series. Can’t get more than halfway thru. Can’t restart in the middle. Ugh.
Another vote for Ulysses, although I want to try again because it’s weird enough to be intriguing although incomprehensible. Sadly, also, most books by Dickens. A Tale of Two Cities was easy to read, but trying to read Oliver Twist I just could not get past the ironic social commentary. If he would just occasionally write what he means instead of the opposite 
LoTR was hard to get into the first time, at 9. I read the whole thing, but had forgotten the beginning by the time I got to the end. On repeated rereadings, however, I became a convert. Also have the Bible on continual rotation, and recommend Ecclesiates to snarky cynics and sceptics. You can’t out-snark or out-sceptic that dude.
Mrs. Dalloway. I had to read it for class in college and managed to present on it without having read the whole thing. It’s so awful.
I read the first LOTR book. The Fellowship. I don’t think I’d be able to get through the rest. I’m just so not into Tolkien or fantasy or dwarves. Especially dwarves.
I re-read Ulysses every year, starting in June. :o
I was just this morning (while making breakfast, appropriately enough, though not a kidney) thinking about “Afraid of the Chookchooks” as a band name.
I finished Gravity’s Rainbow, but I can honestly say that if you’ve read about halfway through you’ve basically read it - there are events that occur in the plot later, but it’s definitely more about ideas (and writing) than plot, and those ideas are pretty much played out by the halfway point.
The ones I can’t finish are A Confederacy of Dunces and Lolita, both of which bore me to tears every time I make the effort.
A quick check of my ‘ditched’ Goodreads shelf shows way more of these than I thought:
Go Down Together: The True, Untold Story of Bonnie and Clyde, by Jeff Guinn
Inheritance Of Loss, by Kiran Desai
Pride and Prejudice and Zombies, by Seth Grahame-Smith
Tree of Smoke, by Denis Johnson
Privatopia: Homeowner Associations and the Rise of Residential Private Government, by Evan McKenzie
The Center Cannot Hold: My Journey Through Madness, by Elyn R. Saks
Blasphemy, by Douglas Preston
Blue Heaven, by C.J. Box
Swann’s Way, by Marcel Proust
Wickett’s Remedy, by Myla Goldberg
American Psycho, by Bret Easton Ellis
The Kite Runner, by Khaled Hosseini
The Great Influenza: The Epic Story of the Deadliest Plague in History, by John M. Barry
Pattern Recognition, by William Gibson
Mister X, by Peter Straub
Almanac of the Dead, by Leslie Marmon Silko
Jonathan Strange & Mr. Norrell, by Susanna Clarke
One Hundred Years of Solitude, by Gabriel García Márquez
I am a feckless, restless, impatient reader.
Stephen Donaldson’s Lord Foulsbane series.
Just…can’t…do it. And I’m not sure why. It’s not the subject matter, as I’m generally into dark fantasy, but…jeez. Just…slog slog slog. It doesn’t resonate at ALL, and I did finally make it through the first one; even GOT the second one. Just…can’t open it. Bleargh.
I’m kind of surprised – you and I usually have fairly similar tastes, and those are two of my favorite novels.
My answer is Lord of the Rings. I’ve tried a few times, because, for some reason, I feel like I should have read those books. But I find his writing style incredibly tedious. I’ve never even made it through the first one. I did read The Hobbit, but I really didn’t even enjoy that one very much.
Tar Baby, by Toni Morrison. Odd, because Song of Solomon is on my desert island list, and I liked Sula as well. Odder still that I’m told this is the case with almost all women. Even if they love everything else Morrison has done, Tar Baby is anathema to women. I don’t know if it’s offensive or otherwise disturbing, because I can’t get far enough to gauge it.
Though I’ve read virtually everything Sinclair Lewis ever wrote–including The Prodigal Parents, Work of Art, Our Mr. Wrenn, and The Man Who Knew Coolidge, I must have started Dodsworth half-a-dozen times or more, and never got past the first hundred pages.
I also found Lord Jim to have about a short story’s worth of material, padded out to impenetrably repetitive novel length.
Funny novels such as Catch-22 also have trouble maintaining their pace throughout their length, brevity being the soul of wit, and all . . .