What is the most important thing to have with you if you were alone on an island?

Infinite water supply

Rum

weapons to help me getting food, killing animals, making fire, and against other people that could live there too.

That depends on if I have hope of getting back, say if I had some contact to the rest of the human race, but in most scenarios, if I am to be alone on an island, I would want a gun with a single bullet. I would take my own life before the loneliness does.

Ham shank.

Helicopter......

Unlimited supply of duct tape.

My cellphone :-)