LotR is a great story but let's face it, the writing is second rate. Anything by Austen is first rate writing, but her stories are slight. Homer did not write novels. I love Dickens, but he wrote potboilers. (The first chapter of Bleak House, though, is perfection.) Mark Twain blew it when he let Tom Sawyer take over Huckleberry Finn. Middlemarch is a contender but think the prose is dated. In Search of Lost Time is a hell of a read in English & makes me wish I knew French, but it is at the very edge of the novel form and too long for most readers. Ulysses too much of a game. (But the last chapter- wow!) Don Quixote is a worthy nominee, but is too fantastic to be a novel in the sense of having a believable story line. War & Peace is too didactic. Anna Karenina is good but dated. Crime & Punishment is wonderful but is a young person's book. Brothers Karamazov is too weighted down by religious concerns.
I second the nomination of Moby-Dick. It is a ripping yarn, worthy of Conrad, but it is also a very modern book despite its age. (Check out
http://damionsearls.com/book9.html for a surprising aspect of this book, involving a kind of reverse abridgment of the book called "; or The Whale.")
To me, a classic book is one which you can read at any age, or every age, with not only enjoyment & entertainment, but intellectual profit. M-D seems to me to require redigestion each time it is read.
In short, M-D has it all: story, writing, moral introspection, appeal to all ages and both (all?) sexes. Plus you can skip the chapters that don't interest you without much damaging the book.