This question is ridiculous! Not because I won't get trapped on a desert island with 6 books though, because that's happened to me several times already. It's ridiculous because the intention behind the question is "What books would you live on minimalistically?", but the practical answer is "The books I can get the most entertainment out of". Let's not kid ourselves, our favorite books will not entertain us for an indefinite amount of time with nothing else to do save contract malignant melanoma. Our favorite books are our favorite books because we've read them, cover to cover, probably many times. I don't know about the rest of you, but I could reproduce a good portion of the SRD given a sufficiently rambling notebook or complicated system of line drawings in the sand. Why would I bring the core books with me? Maybe I cannot perfectly play D&D with my imaginary desert island friends unless I have the core rules for reference, but they're not going to entertain me. The same is true of any book I have.
Give me books I haven't read, in other words.