If you were abandoned on a deserted island, the items you would need to survive would include acquiring food and water, creating some sort of shelter and any other items that would help you get back to civilization. The most important items for survival are those that will sustain you physically and provide some means to facilitate a rescue.
Flare or Signal for Help
You want to be able to signal for help to planes or ships that are approaching or passing the deserted island. A ham radio may be useful to reach civilization. You can use a flare or use a flashlight to signal for help. Alternatively, you can use a mirror to reflect sunlight to emit a signal. Another option for any planes or helicopters flying above the island is to spell out "SOS" or "Help" in stones and rocks on a beach or any other open area. Create a smoky fire to draw attention.
Food and Water Items
Water and food are absolutely vital to survive on a deserted island. You will need a source of fresh water, as ocean water contains salt, which will increase dehydration. If you can't find a freshwater stream, build a container to act as a rain barrel to collect rainwater for drinking. When you don't have a bucket or pail, use large shells or a shoe to collect rainwater. You will need some sort of rod or spear to catch fish with. A spear would also help you to kill small animals for food. Look for fruit or vegetables on the island to eat if you don't have packets of crop seeds.
Shelter and Warmth
To avoid exposure and hypothermia, you must find or build a shelter on a deserted island. Use a raft, boat or plane for shelter if they're available. A tent would be helpful; however, you can build a shelter from reeds, sticks, stones or logs. Matches to light a fire of twigs and logs will help to keep you warm. Though any material to help keep you warm would be beneficial, consider a sleeping bag, blankets and articles of clothing for protection against the elements.
Most people would not have the knowledge to survive on a deserted island for very long. One of the most useful items to have in that situation would be a book or manual on survival tips. The book should include how to build or find shelter, how to hunt and fish, what water is safe to drink, how to build a raft, about poisonous mushrooms/plants, what kinds of fish not to eat and how to defend yourself against wild animals.