Knife / Machete
A survival knife is arguably one of the most useful items you can have with you while you are in a survival situation. A knife is a tool that can do just about everything you could possibly need on a island, it can clean game, build shelter, open food rations, start fires, and help build any other tool that you could possibly need. It is by far the most versatile tool that you can have with you.
Water Storage / Purification Kit
Water is imperative to your survival and without it you will be dead in under 4 days. Most of us take water for granted we can turn a knob and fresh clean water comes out, but if we were ever in a survival situation water could become a big problem. With a water purification kit we can find water and turn it into clean drinkable water.
First Aid Kit
First aid kits can help when ever you get a injury. You don't want to attempt to survive with open cuts or infections that could end up making your situation 10 times worse. First aid kits include gauze, bandages, alcohol clean wipes, gloves and other supplies.
Fire Starter
Fire can help you in so many ways when deserted on a island, it can help keep you warm on cold rainy nights and can cook food you find to keep you healthy and surviving. The most important thing fire can do it to boost your moral and help you mentally know that survival on a island is not a impossible task.
Rope
Rope can be used to for a number of things when deserted on a island. Maybe one of the most important things being catching fish, splitting a rope in half and attaching a hook can be a efficient way to catch food for the night. Another use for rope can be building a shelter, rope can help you tie together large branches and provide a base for your home.