Boy, lots of possibilities here.
I, too, found The Lord of the Rings memorable and compelling. I long ago lost track of the number of times I’ve read it through. I used to read it about once a year.
I was blown away by The Odyssey when it was assigned reading in junior high. We got the full Robert Fitzgerald translation, which I devoured. I was also assigned it for a freshman humanities class, and have re-read it multiple times since, to the point that my paperback copy is falling apart. I have a copy of the Robert Fagles translation on both cassette and CD (for some reason, I never found an audiobook edition of the Fitzgerald translation), and I’ve lost track of the number of times I’ve listened to it all the way through. I feel similarly about The Iliad (for the same two translators), and have re-read it multiple times. For some reason, the audiobook of Fagles’ translation is grotesquely abridged, which is too bad. But I prefer the Odyssey to the Iliad.
I find I can easily get hooked and re-read Frederick Forsyth’s thriller The Day of the Jackal. I like Forsyth’s other books, as well, but none as much ass this one. Again, I’ve lost track of re-readings. Wonderfully told and detailed.
Similarly, I have constantly re-read C.S. Forester’s “Hornblower” series. No other set of sea stories affects me that way – nor O’Brian or Alexander Kent. I like Forester’s other works, too, but the Hornblower books, possibly because he let Hornblower always succeed , or at least come out well, rather than the way many of his other books have pessimistic (if realistic) outcomes. Many of Heinlein’s books have the same effect, including the above-mentioned Moon is a Harsh Mistress. I have three Heinlein books on audiodisc, and re-listen to them frequently.
Mark Twain’s A Connecticut Yankee in King Arthur’s Court and Life on the Mississippi. You can keep your Tom Sawyer and Huck Finn – this is the real Twain.
I asked for and received a copy of Jonathan Swift’s Gulliver’s Travels when I was still in grammar school, and it’s another book I have frequently re-read. I’ve got an Annotated edition, with annotations by Isaac Asimov, which was a great help in understanding several of Swift’s references.