I’ve read plenty of books more than three times - in fact, my current read is a book that I’ve read over and over again, JM Roberts’ History of the World. It’s one of those books I like to take to restaurants and read while eating… as a matter of fact, I’ve found restaurant receipts from 1994 and 1996 in this book, and will probably find one or two more.
I’m not much of a re-reader, but I managed to get assigned Achebe’s Things Fall Apart three times during my school career. First time was in an “Afro-Asia” centric 9th grade social studies class. Then in 12th grade AP English (at a different school). And once again in college in the locally famous “African Storyteller” class at UW-Madison.
That is a truly excellent book, and I have read that twice. Except my copy is called The Penguin History of the World, by JM Roberts. Published by Penguin Books, of course. I trust it’s the same book.
Gone With the Wind
The Oz Books
The Masters of Rome series (Colleen McCullough)
The Thorn Birds
Earth Children series (Jean Auel, and I doubt I’ll read the last one)
The Kent Family Chronicles (John Jakes)
North and South (ditto)
Most of the Stephen King books (except for Cujo. I could only read that one once.)
The Outlander series (Diana Gabaldon, the newest one left the Amazon warehouse yesterday afternoon)
Harry Potter
Tom Sawyer
I think there’s more, but that’s a start.
I also read through relevant sections of the Lonely Planet Thailand guide when a new one comes out every two years like I’m doing now, just to keep up to date on tourist stuff. But I don’t think that counts, because I don’t read the entire book, and I don’t reread the same edition.
I rarely read a book twice, but three that come to mind that I have read many times:
Lord of the Rings Trilogy (six times and counting)
Catcher in the Rye (14 times, been there done that - ah, youth.)
The Front Runner (Twice because I liked it, 2 more times for a film studio project development that didn’t happen - was supposed to star Paul Newman!)
First allow me to say that I officially love everyone posting to this thread and this whole site! I have lurked around SD for a while reading Cecil’s stuff, but never really thought of joining the message board, until today. Look at all you re-readers - you make my heart swell with joy! 
I have read numerous times:
Atlas Shrugged (and still love it)
1984
Animal farm
Just about all the Stephen King books
Anne McCaffrey’s Pern books
Mercedes Lackey Valdemar books
Raymond Feist Midkemia books
Harry Potter 
and a lot of other fluffy SF/FAntasy stuff
Yes, it is the same book.
Adams’ Hitchhiker’s Guide to the Galaxy; Asimov’s Foundation Trilogy; Heinlein’s Stranger in a Strange Land, Farnham’s Freehold, and Podkayne of Mars; Louisa May Alcott’s Eight Cousins and Rose in Bloom; and Swiss Family Robinson. (Also Pokey Little Puppy and Three Billy Goats Gruff and various fairy tale collections, especially Shoemaker’s Elves and Twelve Dancing Princesses :D))
ETA and a bunch of Bradbury, especially Dandelion Wine
I forgot about all the Sherlock Holmes and all the Poe I read in school, and re-read. Otherwise, I’m really not much of a re-reader.