You’re Stranded on a Desert Island (not dessert)

Tarp - this is the single most useful item. It can be a shelter, it can collect water, and it can be used to distill water if you don’t have rain water. That’s just getting started.
Hiking Boots - Your mobility is super important for seeking resources. Boots are very repairable as well.
First Aid Kit - Preventing infection is going to be one of your greatest challenges. There are other ways to do these things in the field but having a GOOD first aid kit is going to save your life.
Knife - The 2nd most useful item. It’s a tool for construction. It can make other tools. It’s a weapon for self defense and for hunting. Again, that’s just getting started…

Honorable Mentions:
Handsaw - Can be used to make other tools or structures. However it will wear out much easier than a knife.
Flare Gun - Great for signaling a potential rescue vehicle, but you get only as many chances as you have flares.
Volleyball - Everyone needs companionship. But those friends tend to drift away.

Why I didn’t include other items:
Sunscreen - Can be made on site. Also, you already have a tarp.
Toilet Paper - extremely limited and can be replaced with many other items. At a minimum you can wash your butt in the sea or down stream.
Pot - useful but also something that can be built on site.
iPod - Only good for the first couple days.
Inflatable Raft - Assuming an island in the middle of an ocean, you are at great risk of dying if you hit the sea. It’s better to stay put. The raft does have other uses but most of those can be done by the tarp.
Flashlight - Useless after the batteries die. Also, fire is a thing.
Insect Repellant - can be made in various ways.
Hammock - a nice to have but they wear out eventually and there are other ways to get yourself off the ground when for sleeping.
Compass - Only needed if the island is very large. Also, you can setup a makeshift compass at night using the north star.
Mirror - Useful for signaling rescue craft from a long distance but there are other ways to do this as well.
Vitamins - Definitely useful in the short term but you’ll eventually run out. Better to know how to forage for nutriants.
Water Purifier - A luxury item when you have the stuff needed to distill water.
Fishing Rod - Can be made on site
Rope - can be made on site
Rifle - Totally useless without bullets. Even then it’s only good until you run out of ammo.
Weed - Too limited in the amount.
Tent - replaceable by the much more useful tarp.
Matches - Too limited of a resource when there are so many other ways to make fire.