Hmmmm, interesting to think about and I loved reading everyone else's answers!
If we're going for
desert island-specific choices and not favourites, then:
General Music (who buys actual CDs anymore?)
:
Dead Can Dance - for
beautiful,
haunting, and sometimes oddly
calming music
Tchaikovsky - for an
emotive,
decadent Russian Romantic with
wide range
Simon and Garfunkel -
musical valium 
Movies:
Equilibrium - for
this scene and
this scene (<--- spoilers - if you haven't seen it yet, do!). Think 1984 meets The Matrix.
The Hours - for the literary aspect and also it feels very much like a "woman's story" (in all the best ways). I love how delicately and kindly it treats its characters. Plus, that soundtrack is beautiful.
Away We Go - for a fun, fairly light pick-me-up
Books:
Wittgenstein's Mistress - David Markson
The God of Small Things - Arundhati Roy
plus...
The Book of Longing - Leonard Cohen
OR
Blood, Marriage, Wine, and Glitter - S. Bear Bergman
OR
The Grapes of Wrath - John Steinbeck
- can't decide between the last three
Character:
I've never actually seen Gilligan's Island, so... hmmm, based on the character descriptions via Wikipedia, I'm going to go with
The Professor. He has a background in botany and was a science teacher, so he'd be a useful companion (plus, I could scratch off a botany/survivalist book from my list). I bet he's also a really interesting 2-am conversationalist. :-)