I also do not read a book twice. In fact of all the books I've read, save the Bible and a few other religious books, the only ones read 2 times or more are the first eight books of David Weber's Honor Harrington series and his "Apocalypse Troll."
Here are some of my non-genre books.
Treasure Island, by Robert Louis Stevenson.
The Thirty-nine Steps, by John Buchan.
The Half Hearted, by John Buchan.
The Sign of Four, by Sir Arthur Conan Doyle.
Pickwick Papers, by Charles Dickens.
Great Expectations, by Charles Dickens.
The Mayor of Casterbridge, by Thomas Hardy.
Rogue Male, by Geoffrey Household.
The Lord of the Flies, by William Golding.
The Shepherd, by Frederick Forsyth.
The Guns of Navarone, by Alistair Maclean.
And three nonfiction books.
The Colditz Story, by P. R. Reid.
The Latter Days of Colditz, by P. R. Reid.
The Great Escape, by Paul Brickhill.
The Loved One by Evelyn Waugh. It just appeals to my cynicism.
Brideshead Revisited by the same author.
Read it too, and probably more than once come to think of it.Waugh! How about A Handful of Dust? I've read that one seven times.