Quick/agile, smart and tech-savvy I'd say are my main skills. I'm not super pumped but I'm not a weakling. I've never been in a fight but I think I'd do well. I got to blue belt in ju-jitsu when I was younger so I have good balance/posture and know how to properly punch and throw/grapple people (I feel it is one of the better martial arts as it deals with more realistic situations, plus it has a load of weapon training, still got my nunchucks). I've climbed the tallest mountain in the UK (which isn't really saying much tbh, though I did it quickly) and can bike a long distance at my own pace, so I'm fairly fit. I have fired a rifle at a shooting range (once) and have been taught how to clean/maintain a gun (but forgot most of it), but they won't likely be useful skills in the UK. I have flown a powered aeroplane but not the take off or landing. I know about electrical circuits and stuff, probably enough to fix most broken tools but never really been able to put it to practice. I have some basic medical knowledge. I am very good at stuff on computers (learn programs quickly, web design, programming, graphic design) but that doesn't seem too good in the post-apocalypse.

Pretty much I have a lot of theoretical knowledge and some guesswork but not a lot of actual practice. However I learn things quickly, have excellent organisational skills. If there were no other people stepping up for the leader role I'd be confident enough to take charge but I'm not really a strict or commanding person. What role I would take in a group would depend on the others; mostly I like to flit around doing odd bits and bobs and helping others. If I had to pick a role it would be organizer and designer/inventor. And the place I'd choose to bunk up would be a library, to preserve the knowledge and learn more survival skills.

If necessary, I will take it upon myself to repopulate the earth. Even if it's not necessary, I'll do my damndest.
Also, I have the vital ability of being able to place myself in a leadership role and have everyone accept it, without actually contributing much of anything.

I had the ability to accurately hit stuff with a bow from a hundred meters away. Note the had part, that was before my right eye became ♥♥♥♥ and I now have to get by using my left.
Have spears and ♥♥♥♥? that might help?
Reasonably strong but not the bench press 200 pounds strong, more the black eye punch strong, or break own finger punch strong.(Failure incarnate...) I do have reasonable martial art skills, Judo/karate/boxing stuff.
Can bike incredible distances though, at a good pace.
Never shot a gun since they are illegal here.

So, dead weight compared to most of you.....

I'm mostly lookout material.
Give me a gun, put me in lead, I guarantee to scare off anybody and everybody that tries to talk to our group.

I guess how well you guys would do post apocalypse would depend on what caused it.
definitely zombies

In response to David's post.
If zombies.
I shoot everyone.
including the group

I can run very quickly but not for long and am kind of out of shape physically.
I can go very long periods without consuming anything, but it doesn't mean I don't at all.
I'm a good shot with firearms, and know how to clean them, however I can't repair or mess with them in any other way.
I can lead well and am not constrained by morals. If killing a member of my party will result in the survival of the rest of the team, I would be the one to pull the trigger. To add to that, I am very emotionally strong and stable. Despite sounding heartless, I like to think this allows me to morally support my group as well, as I would spend less time grieving and more being motivational and planning our survival.
I know how to start fires and cook food.
I know how to find good shelter.
I know very basic medical procedures.
I can do very basic technological/engineering fixes.
I am nimble and flexible but have little stamina.
I could probably defend myself in close quarters if I had a weapon, but wouldn't do so well otherwise. I can take a lot of hits, but wouldn't be able to dish out quite as many.

Let's see... Went through BLS emergency medical training twice as well as some other medical-related tasks, and I've a pretty good grasp on anatomy and physiology. Whatever I don't know off hand, I keep half a dozen text books around for reference.
Unrelated to the above, I can prepare animals for consumption.
I already live off two light meals a day.

Downsides: I don't like touching real guns (or potential lethal violence in general), I'm terrible at math, and I don't do well in the cold.

I suppose the skills depend on what sort of apocalypse this is.

Well, I can sprint fast for medium distances, and I'm also very strong and tall for my age, and I love fighting, I'm pretty good at it. I'm also great with fixing electronics, as well as being able to bike for long distances, and even in rough terrain. But, I've never shot a real gun, or know much about them.

I also have an excellent sense of direction, am extremely resistant to heat, just yesterday I rode my bike in 110 degree weather for a few hours. As for other weapons, I'm good with bows, and excellent with throwing knives, I am also brave and usually take the lead with most situations.

I can also take more serious physical wounds without emotionally or physically spazzing out.

As shown in some RtD's, I have a good knowledge of anatomy and tactics, too. Woot.

I've done karate/jiu-jitsu since i was six, so i can handle myself in hand-to-hand combat pretty well (not that it'll be of any use against zombies..). I can run long distances (record: 7 kilometers/4.34959835 miles). I'm good at chemistry (making gunpowder is fun!)
I can make some DIY weapons etc. bows. I can make explosives (molotov coctails, grenades, that kind of stuff).
I don't need too much of food, but i'm always thirsty. I'm not good at firearms. I'm resistant to heat ( our sauna is sometimes at 120 degrees Celsius and no, we don't stay there too long and yes we take a ice-cold shower after that.), I know first-aid, and i'll have no trouble killing another human (i think).
I'm also extremely patient.

I think i'd be the melee/explosives guy

If your sauna is 120degrees centigrade you'd be dead. Even half of that is uncomfortable.
That said, I think I have to use a capital I when I'm talking about myself....

And I'm surprised they teach jiu-jitsu to kids of that age, here it's illegal to kids under 12 or so.

As far as worthwhile and relevant skills go, I've got some decent experience in woodworking and firearm use/maintenance.
I'm also decent at drafting and designing things, but a group would have to be pretty big for that to become relevant.
I like to think I'd have the aptitude to learn more skills well under a situation with survival as the motivation, but who knows.

I'm pretty awful in that regard too, not someone you'd want to send out to go get supplies and come back with them.

You've never been to a Finnish sauna have you?
And yeah, i was kinda suprised too when they took me to the group. I wasn't allowed to take part in all of the cool stuff ( Throws that could do some damage etc.) untill i was like 10 though

I have extreme patience both dealing with friendlies or when staking out enemies, I can stay still and quiet for long times have exceptional grip strength and know how to grapple/fight hand to hand. I would be a positive person to be an ambassador to other survivor groups while planning how to overthrow them if necessary.

I can handle shotguns or Bows and are fairly decent with either.

I have a baseline very low expectation of the post apocalyptic world and survival chances from watching too many zombie movies and hence am able to take pleasure in the little things and will enjoy everyday to the fullest smeshing Zom's in the head.