Of course, the castaways on Gilligan’s Island had an amazing amount of stuff in their luggage. But let’s assume you’re limited to a single regular-sized suitcase. No electronics; they’ll all be fried by the lightning bolt that hits your plane and causes you to be shipwrecked, alone, on a Gilligan’s Island-type isle.
What do you bring?
One of those thousand-pages SAS survival guides would certainly come in handy, along with several thousand waterproof matches.
And a flare gun. And a mirror. Basically anything that’ll help me signal planes and ships and survive in the short-term would be fine. I’m not looking to stay long enough to build a studio so Ginger can have a screen test, after all.
Why bring anything? Just wait a week for somebody else to arrive, or for a Russian space probe to land, or for a pop band to seek to escape their fans. Then don’t screw up the rescue effort like Gilligan always did.
I think I could fit Mary Ann in that suitcase if I put some breathing holes in it.
Assuming I’m wearing appropriate clothing for the situatation as well.
Leatherman-style multitool
Hatchet
Rain poncho–will also make a blanket/sucshade/shelter roof/groundcloth/raincatcher/etc/etc/etc. Heck, I’ve talked myself into taking two.
Floppy hat
Couple reels of fishing line plus box of fishhooks of all sorts
Set of nesting stainless steel bowls
3-4 extra sets of prescription sunglasses
Magnifying glass/firestarter
Small mirror
Little set of tweezers/scapels/sewing needles
Cable saw–won’t take up much space.
Heavy duty water bottle/canteen
Couple of those ultrathin reflective mylar blankets that fold into tiny little 1x2 inch packs
3-4 pairs of Aquasox style shoes…gonna be doing a lot of beachcombing and protecting your feet from jagged coral/lava/spiny critters is gonna be big.
Suitcase is starting to bulge at the seams at this point, so I’ll leave it at that.
Oh wait. A deck of playing cards. So I can sit down and start playing solitaire, and pretty soon some numbskull is going to walk over and tell me to play the black ten on the red jack.
*This is our premier steamer trunk, it’s all handmade, only the finest materials. It’s even watertight, tight as a drum. If I had the need, and the wherewithal, Mr. Banks, this would be my trunk of choice. *
Of course I would have four of these.
Antibiotics? Especially if you get scratched with coral…
I notice I don’t really have any consumables on my list. I suppose that means that unlike Bryan I assumed that I’d be stuck on this godforsaken island for years. No point in taking a tube of antibiotic cream if it will all be gone in a month.
May you live to be a thousand years old, sir.
Just let me have one of these and I’m good.
Need a volleyball. 
You sure I can’t take an EPIRB? Damn.
Add a solar still and fire starter to Lemur’s list, and I’d be pretty happy. Bungee cords also have multiple uses, one would be creating a fishing spear. A few of those would be nice.
Yes, the Mosquitoes were a rockin’ bank. You could steal their electronics after a few good shows which doesn’t violate the OP. A still would be very good. Clothes wouldn’t really be much of a problem. Carhartt work clothes are virtually indestructible. A couple of sets would be good for years. I like a good Swiss Army knife so their Champion version would work. I would vote for a machete as well. You need a good fire source so a flint and steel might be the best if you get drunk from your still and piss all over your matches. That is the leading cause of death among people that get stranded on a dessert island. You might want a pair of swimming trunks and a spear although we all know that doesn’t work worth a damn but it gives you time to drink from the proceeds of your still. I would also recommend a copy of Finnegan’s Wake because no one knows what it is about and you could make it years before figuring out up to page three.
All you need can be delivered by FedEx.
Given my complete lack of desert island survival experience, I like the SAS handbook idea. Knowledge would be key to early survival. If you have to work everything out for yourself, you’re more likely to die trying. After that, you most need things that can’t be found or improvised on the island. I’m thinking edged tools and long term fire lighting gear.
Nobody has mentioned a basketball.
You gotta have something to talk to, while away the hours and all that
I think a volleyball would work better. 
Not at all, the volleyball couldn’t talk back.
Rumour has it that basketballs can
A suitcase seems a very generous allowance. I’m spoilt for choice.
I’ll have:
-A couple of 3 metre square woven plastic tarps - a red one and a blue one
-Several balls of nylon twine
-Edged implements: A small, sharp hand axe, a machete, a knife in the Crocodile Dundee style, and a Victorinox tomato knife (which is useful for other things than preparing tomatoes).
-A set of stainless steel cooking pots with lids
-A stainless steel water bottle
-A wide-brimmed hat
-Stout boots and a pair of crocs
-Antibiotics (I don’t care if they will run out sometime - that only means they’re useful, albeit finitely)
-Fishing kit
-Fire lighting kit would be handy in the short term (I can cope without though)
-Several pairs of glasses (including prescription sunglasses) - my eyesight is, I think, the most likely thing to let me down in a survival scenario. Better have some prescription swimming goggles too.
-A beach towel - brightly coloured and large enough to serve as a blanket if required.
-Whatever practical clothing will fill the remaining space
-Cracks and gaps between the nested cooking pots, etc, will be stuffed with as many clear plastic bags/sacks in assorted sizes and grades as will fit.
If there’s still time, I’d slip in a few packs of seeds - tomatoes, pumpkins, onions - anything else that tolerates a fairly wide range of climates and has the potential to run wild.