I've re-read too many novels to list, but here are a few favorites that I continue to read over and over:
Zen and the Art of Motorcycle Maintenance, by Robert Pirsig
The Mouse and His Child, by Russell Hoban
Riddley Walker, by Russell Hoban
Little, Big, by John Crowley
The Chronicles of Narnia, by C. S. Lewis
The Horse's Mouth, by Joyce Carey
The Wind in the Willows, by Kenneth Grahame
There Are Doors, by Gene Wolfe
The Princess and the Goblin, by George MacDonald
The Princess and Curdie, by George MacDonald
Ubik, by Philip K. Dick
Do Androids Dream of Electric Sheep? by Philip K. Dick
Wow, lots of fantasy, science fiction, and children's books!
I've re-read books, or parts of books, quite often - but not in sufficient number to fit Rich's 'strict' requirements. There are huge numbers of books that I 'intend' to re-read, though ... so you could call me a phantom re-reader, I guess. Strange, I can distinctly remember multiple readings of my 'schoolgirl' series (Malory Towers et al.) and the pleasure I got out of them. The details have been replaced in my over-loaded memory by more mundane things.
I used to reread novels (Anna Karenina, Gone with the Wind, Dickens, Jules Verne come to mind) when I was young (a half-century ago), but nowadays I reread only by accident--halfway into the first chapter, I recognize a character or event and check my database to find that I had read the book 10 or 20 years ago. Like Ruth, I find that I have forgotten enough details to make rereading some mysteries entertaining. I'm planning to go back to Dorothy Sayers when I finish some Agatha Christies on my iPhone.
I've reread many novels over the years, sometimes several times - the Hobbit/Lord of the Rings books and including Dorothy Dunnett's Crawford of Lymond series, anything by Madeleine L'Engle, several M.M. Kayes come to mind immediately, but there are many others. I always notice or learn something new, and usually figure out some arcane detail that I missed or didn't understand in earlier readings. Sometimes I'm just revisiting a fictional world that I love, sometimes I'm looking for certain phrasings and sections that I most admire, sometimes I'm trying to re-evoke whatever the novel made me feel the first time I read it. I even reread mystery novels, and have found recently that I don't remember as much about some of them as I expected, so not only do I enjoy re-meeting certain characters, but I still get to be surprised by the endings.
There are many novels that I have read numerous times during my life, books such as the Good Soldier Schweik I have read at least 20 or 30 times, as well as most of Kafka's work, which I have read dozens of times. Further, I also reread quite a few thrillers that for one reason or another appealed to me, these would be in the dozens as well.
As I am 68 years old, and have been a fervent reader for most of those years, and have a collection of at least several thousand books, both paper and electronic, I can say that I have read an enormous number of books, and as I say, any that I particularly enjoyed or liked, I will often reread a number of times.