The list is a little archaic and location dependent, but I'll have a go at this checklist.
Use basic tools - This I can do, but only because of my experiences with woodworking in highscool and helping my dad build a few fences.
Build a fire [Owyn_Merrilin] - I can't see myself needing to know this unless society colapses.
Swim [loc978] - Check. This is sensible enough.
Sharpen a knife [Owyn_Merrilin] - No idea.
Fish - I'm not a fan of fishing.
Hunt [Dr_Horrible] - Pfft. The only people around here who hunt own estates and have posh accents.
Gut a fish/skin an animal - I prefer to have my local butcher do this seeing as how they have trained for this.
Ride a horse - Bit anachronistic, isn't it? I'd say it's more of a niche hobby than a required skill.
Pitch a tent - Not much of a camper.
Perform first aid, including CPR - This would be useful. It would be worth knowing this but I don't.
Cook a few easy recipes - Egg is a versatile food.
Operate a grill [AGrey] - I tend to use the hob more but the grill can't be too hard.
Know at least one good year for wine - Not a wine drinker.
Build something - I'm pretty good working with wood, and I built the computer I am typing this from.
Repair your possessions - Quite a lot of my possesions are far too complex to be repaired by a layman (electronics etc).
Sew [Sope] - Fairly useful but not essential. I'm alright at sewing, we had a few lessons on it during Home Economics at highschool.
Know how to grow a decent garden - As I said with horse riding, this seems more like a hobbby than an essential skill.
Install/repair basic electric utilities - I can correctly wire a plug and fit a lightbulb but that's as much as I know.
Install/repair basic plumbing - I'd give it a go but I can't imagine I'd have much sucess.
Change a light bulb - Covered earlier. Seems a little odd that this would be mentioned since it's so simple.
Fire a gun - I'm neither a farmer nor rich, which puts me squarely outside the demographic for legal firearms in the UK.
Throw a punch - I'd prefer to take the "flight" option.
Take a punch - I'd rather concentrate on not being hit to be honest.
Read - My apologies my good sir, I didn't realise you were from 1900. Aren't literacy rates at 99.99% in the western world nowadays?
Read/watch the news [Da Chi] - Knowning what is going on in the world is important. Check.
Read a manual [LadyMint] - Sensible enough. Unless the manual is as thick as a novel of course.
Clearly communicate an idea [gmergurl] - Sure.
Talk to others - Check.
Talk to someone you're attracted to (not just cheesy one-liners)- Check.
Know what they're talking about (Literature, art, music, history, politics) [Kukulski] - I'm not particualrly well versed in any of those subjects. I'm more interested in technology.
Drink (Not to excess, but know your preferences and limits) (including whether you drink at all) - I'm a very occassional drinker, and I never drink for pleasure. People can't seem to wrap their heads around not drinking where I live, so nursing a pint of cider keeps them quite for the most part.
Sing or play some kind of instrument (it doesn't matter if it's a kazoo or a violin, learn something) - I'm not musically inclined at all. You'd have more luck training a chimp to play the piano than me becoming competent with an instrument.
Dance - I dance about as well as Commander Shepard.
Play Chess (just know how the pieces move, you don't need to be a grand master) - I'm alright at chess.
Play poker - Does Texas Hold-Em suffice?
Drive a car (automatic and stick) - Perhaps in 10 years when I have managed to earn enough of this elusive thing that people call money.
Ride a motorcycle - I'd rather drive a car.
Operate a boat (canoe, yacht, sailboat) [loc978] - I live about 7 miles from the sea, but I cant forsee any reason that I would need this skill.
Jump start a car - It's something I'd take the time to learn while I was learning to drive.
Change a tire [Wadders] - Same as above.
Change the oil [Athol] - Again, same as above.
Clean yourself - Sorry, keep forgetting you have been skipped 100 years forward.
Clean your possessions ~[PettingZOOPONY] - Erm. OK I guess.
Shave [Armored Prayer] - Essential, unless you rock a beard (and even then you'd still hopefully trim it).
Tie a tie [Wadders] - A must in the world of business.
Polish their shoes [Lord Kloo] - Not as essential in the world of business, but it makes a good impression.
Open a can/bottle [Irriduccibilli] - Check.
Twist off a lid - Check.
Pack a suitcase [Ledan] - I'd say I'm competent at this, but not great.
Pack a car [Ledan] - My family hasn't owned a car for about 12 years. I imagine it can't be too difficult though.