I feel exceedingly lame... I haven't so much as seen a copy of Tom's books, let alone read and reread them. I am a poor college student in the States, after all. Most people around me look at me myopically and say "Who is that?" when faced with my geek fangirl tendencies. I know, sad. Its hard to be cool around here.
Anyway, in lieu of having them, I guess I would grab my copy of Catch-22 since I love it about the best. I try to reread it every year, finding new things every time. I'd also grab Stranger in a Strange Land while I was at it, and my complete works of Edgar Allen Poe... I would grab Arthur C. Clarke if I had any, however I do not. Most of my books are things I found in the Libraries Discard pile.
But the book I would never leave in my house, the one I would grab before my Tolkien or my Adams or my Rowling books, would be John Lennon's In His Own Write. I love to sit and read it aloud to myself. At one time I had half of it memorised and would quote it to annoy people. Alas, apparently it actually did annoy people and I quit, now I don't remember it so well. But still great fun.
No! Wait, I forgot, the book I couldn't survive without would be The Hypochondriac's Guide to Horrible Diseases You Probably Already Have.
I named my phone "Tom Baker's Face" for the practical reason- I now get to say "Damn, Tom Baker's Face is ringing, give me a sec," and other such awesomely weird things.