I would be a prize food resource. I bring to the table a well balanced portion or muscle and fat. While older I feel I can deliver a quite satisfactory meal if properly marinated and then slow roasted. Plus the drippings can be used for soap, wagon wheel lubrication. and host of other uses.
Uh, let’s see - vegetable gardening, sewing by hand or on a sewing machine, knitting, knowledge of how to make a little go a long way (raised by very frugal parents).
I was also a medical lab tech in another life - I could brush off those skills, I guess.
I’m pretty good at reverse engineering stuff, to wit I can fix a machine that I never saw work properly in the first place.
My accounting skills would enable us to calculate how rapidly we were going to starve. Does that help?
Honestly, I don’t bring much in terms of specific skills, but I do have a smattering of amateur DIY and garden skills and enough physical capability that I’d be useful assisting in lots of areas.
HAH! 
But hey, post-apocalyptic society always needs a few redshirts to do things like “Check out that partially collapsed building” or “Go meet with the leader of the rival clan, the one with the guns and tatoos”
Brewing and distilling
Camping skills
Competent archer
Better rifleman
Adequate shade-tree mechanic
Good cook
Basic survival skills - fire-starting, knapping, shelter construction, etc.
Competent gardening skills
Possessor of a magnificent modular, personalized food-containment unit
Hey, I’m a team player. I’ll make myself useful.
I probably wouldn’t survive my first month without meds. I guess I could die quietly. I used to be an active gardener and also to build furniture, but I am no longer able to do much gardening and, without a supply of lumber I am not going to build much.
Would you please elaborate? I’m hopeful that this is something awesome, but prepared for the answer to be “lunch cooler”
I know how to raise pigs, chickens, turkeys, and ducks. Also butchering of both domestic and game critters.
Navy Rifle and Pistol Marksmanship ribbons, both with an E device.
I was trained as an Armorer by the Navy, so I can fix and modify weapons.
Seabee Builder, so construction skills.
Pretty extensive experience in making and drinking beer, wine, and mead, also fermenting foods.
I’m apparently the only person on the boards who knows how to forage for mushrooms, based on the quick death of this thread.
A lot of the vet skills I’ve picked up are also applicable to humans, and I’ve been trained in Wilderness First Aid, so until we recruit Qadgop, I can attempt to patch people up.
Over decades, I have carefully constructed a truly massive structure of adipose tissue around my abdomen (12 ounces at a time!), providing me with months and months of survival calories should the need arise. Awe inspiring, it is!
I can take wool directly from sheep to wearable item or blanket or whatever.
I can shoot fairly well
Good at growing food in the garden
Very fast learning, so teach me what else you need me to do
I could probably get a high(ish)-solids anaerobic digester going, to convert various wastes into compost and biogas. At least that’s what I’d use the apocalypse as an excuse to do.
Primitive Camping
Wilderness Survival
Foraging
Musician / Bard
Cooking
Carpentry
Good show…good show.
I’m a software developer so maybe I can think really well?
Other than that…I think I’m gonna starve
I have a crapload of survival skills from my backpacking and farming life, but I think that the most usable and valuable skill I have is the ability to mediate between people and help groups form a consensus. Nobody is going to make it through an apocalypse alone, no matter how much ammo they have amassed.
Probably mostly as a thug (i.e. I’ve got martial arts training as well as some survivalist training, some weapons training, etc), though I have some camping skills, as well as some electrician skills assuming the post apocalypse includes having access to generators and such. I’ve never been into hunting, but I’ve dressed and cleaned game before, and I know the basics of hunting anyway. I’m getting a bit long in the tooth though, so not sure how much use I’d be these days. I’m certainly not going to be able to lug a ruck for 20 miles a day or anything like that, but perhaps help setup an enclave and defend it, get basic electrical and sanitary facilities going, etc…yeah, I could probably hack that.
What would be awe-inspiring is if you can maintain the reserve in the face greatly increased activity and greatly reduced intake, like Skipper on Gilligan’s Island, Hurley on Lost, or that large fellow on Revolution. That’s impressive. Not like that wuss on Arrow who caved in to the situation and came back all muscular and with hunting skills. 
I have quite a few skills that would be very helpful after the shit hits the fan. However, since I’m on quite a few maintenance medications, I might live only long enough to be able to teach a few of those skills to others. I’m also really, really nearsighted. Once both my pairs of glasses are gone, I’ll be effectively blind. I’m 56, so even if I still had a uterus and ovaries, I doubt that they’d be functioning.
So gather around, while I teach you all I know about knitting, crocheting, sewing, and how to make patterns. Watch while I show how to start a fire and keep it going with a minimum of fuel. Here’s how to butcher various animals, and here’s how to cook various things, and how to make a tasty meal from scraps of leftover meals.