The Koran. Because I already have the jist of the Holy Bible in my heart/mind. So I could always burn that Koran and know that a whole carpload of civil rights activists would find me reeeeal soon and give me a ride back to the mainland.
The biggest, fattest, most comprehensive, dictionary I could find (the kind that has lots of other stuff to look, besides just definitions). A big, fat, dictionary with lots of stuff in it offers all kinds of "open-ended" word play, memorizing, browsing, and general "verbal entertainment" and odd kind of reading pleasure.
Besides, I could also use it as a little stool to sit on (to make myself feel a little more as if I were in a civilized living situation), a little step-stool (which might be helpful with some things involving trees), an anchor belongings if the island got windy, and any number of handy purposes.
Yes, such a book would be cumbersome and heavy - but, heck, where would I be going anyway? Of course, it might make handy "firewood" if I thought any helicopters might be coming by... Oh, also - the more pages, the more "note paper" there would be if I had reason to want to leave, send, messages anywhere in some way (maybe a Hansel and Gretel type of path if I needed that.)
I actually thought of a phone book too - but I wasn't imaginative enough to imagine a cell phone. I was just thinking a phone book offers lots of potential for word games, idle nosiness, memorizing numbers - and the rest of the stuff a dictionary (from my first post) offers.