Well it depends on the level of vegetation, land animals, local fish, and climate. If land vegetation and animals are low I would take: An inflatable swimming pool Rationale: You can inflate it while it rains to catch water, you can sleep under it, it can float and thus be used as a fishing boat, and when deflated it could be used as a tarp to sundry caught fish on as their is no fire. A roll of garbage bags Rationale:They are heavy duty storage containers with large volumes; can capture rainwater and store it within, cut head and arm holes to have clothes, can be filled with air to supplement pool for boat, could also be used to dry fish on, can be twisted to be like a rope, fill with sand for strong structure, etc. And a net Rationale: catch fish(duh), hold things down during storms, cut off fibers for other purposes. @alecrules - You cheat.
kujo, a laptop wouldn't last long on an island with no power
I would bring: 1. A firestarter. (One that you didn't need a knife to make sparks with.) 2. A lot of rope 3. An axe. I would pick these because I could make shelter. Since islands usually are in the ocean... DUH! I would catch fish or use my axe to cut down a tree with fruit. Eventually, I would make an SOS sign and burn it so airplanes could see it and rescue me.
I would bring lots of lumber, a well-equipped, robotic construction crew, and about 6 truckloads of cement.
The Island would have food and water enough for myself for enough time. Then, take the rorbotic construction workers, the lumber, and the cement, and tell them to build a self-designed 5-star hotel. Next, I would build a small bridge with the remaining supplies to the shore of the mainland. After advertising the hotel, people would flock to the island, where I would be able to buy more supplies.
Or, I could turn it into an insane asylum, for some added fun.