Well, if you mean in terms of "what possession I hold dearest to me" - then it would obviously be my iPhone.
But that wouldn't be much use on a desert island if I didn't have access to the internet/phone network and a source of energy that could charge my phone.
So perhaps a more practical answer would be something that'd help me survive. If there was no fresh water on the island, then perhaps something to desalinate sea water?
If that wasn't an issue, then maybe some sort of weapon to hunt with. I'd probably go for a bladed article, perhaps a spear...
I could use it go fishing (I'd have to learn to spear-fish), defend myself from wild animals.
Actually, on second thoughts, I think I might be able to make a spear out of the natural resources I'd find on the island (if cavemen could do it, how hard could it be?).
In that case, I'd just opt for a gun (would I be able to request ammo to go with it?)