The Lord of the Rings by J.R.R. Tolkien. Definitely. I've read it seven or eight times and still can't get enough of it.
Nineteen minutes by Jodi Picoult. I have read it just once but I loved it. Absolutely.
The Complete Illustrated Works of Oscar Wilde, which I just got from my girlfriend. Wilde is amazing and the book is thick - a lot to read!
The Bible. I'm an atheist, but I have read The Bible once. Though I've been thinking about reading it again - so why not take it with me?
Usko, tiede ja evoluutio ("Religion, Science & Evolution" in English) by Tapio Puolimatka. An informative criticism book about the evolution theory, and a desert island would be a perfect place to read it.