Plastic bags - I favour something a bit tougher than a sandwich bag, and a bit bigger than a sheet of A4 paper - good for keeping partial portions of dry food dry, good for keeping small items of clothing or equipment dry, good for impromptu collection of berries or other wild foods - and probably a hundred other uses.
Antidiarrheal medication. Imodium or Kaopectate are both good choices.
I try to take a camping pad if possible because while I don’t need the padding, the warmth almost always is, since the times are rare where it is both cool enough to comfortably hike during the day yet warm enough not to want insulation during the night.
As someone who spends a significant amount of time off-the-grid and a Scout leader, I should weigh in here.
As mentioned upthread, it really depends on what kind of camping you’re planning, the facilities available, distance, space, weight, and most importantly the WEATHER.
A good sharp knife is mandatory.
1st Aid Kit
Water and water bottle!
Food
Dry matches/lighter
2 headlights/flashlights and extra batteries.
Waterproof pack
Dry change of clothes (extra socks) and dress in layers rather than heavy clothes.
Hiking Boots
A hat and gloves (summer or winter)
Raingear
A Pot
Plate, bowl, cup and utensils.
Depending on weather, etc. Bug repellant and Sunscreen may be a good idea
Fire or Stove? - I prefer a fire for light, heat, and to keep bugs and wildlife away, but a camp stove has benefits too. If you don’t want to have to lug camp fuel around, I recommend a rocket stove, you can buy them or make your own at home or in the field with a log.
The biggest mistake I see people make is tent sizing. Smaller is much easier to pack, carry, and set-up. It will require a smaller level area and will also be much warmer than some cavernous 12-man mansion.
If you’re sleeping on the ground, sleeping pads these days are compact and lightweight and provide great insulation and padding. Do not use inflated air in cold conditions.
A tarp and some rope always comes in handy.
I hate to say it … but today, a cellphone for emergencies could be a lifesaver.
All good ideas =) I lived with a couple different special forces guys and my dad was combat infantry, so oddly I grew up with military gear instead of the civilian equivalent. To this day my current luggage is a molle pack. I helped my guys pack their rucks a number of times, and picked up some habits. I use the large 1 gallon ziploks, and into each one goes a rolled tshirt, bar, panties and socks then I press out all the air. My trousers get their own zippy bag. I have 5 pair of casual trousers, so I will pack the other 4 with the number of shirt packs to equal the number of days I am packing for plus at least 3 extra. I also pack 2 pair of flannel dorm pants and 3 sleep shirts. I don’t actually use a towel, I have a french terry cloth kaftan and a small 'turbie towel’ for my hair. Add a pair ofcrocs [mine are international distress orange] and a spare set of boots or beach shoes [or whatever footgear I need, last time i had a nice pair of dress pumps to go along with my formal gown] and toiletries and I am good.
And yes, I pack like I am going camping even if I go on a cruise ship. Waterproofing the clothing is easy, and if for some reason my pack gets dumped in the water or left out in the rain, I am good to go.
Oh, I also pack a woobie. Woobies are good =)
I still wear a field jacket mrAru got for me in about 1992 or so. I realized when I was wearing it on base last week that it was probably older than most of the guys on base and still in almost perfect condition. I also have the ‘smoking jacket’ liner and use a helmet liner as a hat - I keep the smoking jacket and helmet liner in the SUV along with gloves in case I need to be really warm. At home I have a ‘pumpkin suit’.
I grew up in western NY, and we did a fair amount of fall and winter hunting trips so camping in snow is not a big deal for me, what I freaking hate is RAIN!!! There is nothing fun about being wet and cold, and you can die really fast if you are not careful. With my poncho, a couple poncho liners and a roll of para cord, add in a lighter and my sapirka [shovel and ax =)] I can be relatively comfortable in a camp in a pinch. For real comfort, an improvised camp in a deciduous/evergreen mix woods is amazing. When I was 19 we did a winter camping trip to a spot just outside Letchworth State Park in a friends private hunting spot [he owned about 300 acres, fantastic spot] and set up a lean to against a rock face, rooved over in pine boughs, with pine boughs as the bedding base, adding a small fire reflected in and we were toasty, comfortable and telling stories and sharing coffee and cooking up a couple bunnies we killed. Best weekend with my father and brother ever.
Boots reminded me – hiking boots for me are personally deadweight. I guess if there were a chance of sub-0F weather I would consider them but would skip out otherwise. Air Monarchs, and probably many other cross-trainers, have enough support, and warmth for my needs. The only problem with them is they aren’t very grippy, so if scrambling were in my future I’d wear trail shoes instead. But I prefer Air Monarchs to even trail shoes otherwise since they afford more wetness protection and padding than trail shoes! They are elevated enough that I can cross tiny brooks in them without getting wet and have fallen directly into a winter creek and came out with my socks only damp.
They’re also slightly warmer than running shoes, and also the trail shoes I’ve owned due to the aforementioned elevation and relative lack of ventilation.
Things not to pack, but I have seen at actual campsites:
sledge hammer
bricks for campfire boundary
actual mattress
queen size down comforter
8 qt. stock pot
cast iron skillet
While I wouldn’t use those, I do find that an extra camping pad along with a bedsheet makes it feel a lot more comfortable since when I roll during the night I would neither hit the tent floor nor the sticky camping pad. If there’s not enough room then just a bedsheet is great too although I skip it on hike-in camping.
Yep, I’ve seen some downright stupid stuff.
a steel cooler - I actually saw someone lugging it down a trail… miles from anywhere!
A TV
Large Boom Box radio
5 gallon Jerry can
I forgot to mention:
A lid for the pot comes on handy.
Water purification tablets, while I wouldn’t use them as a primary source, they could be a lifesaver in a pinch.
A mesh bag with rope are handy for drying dishes and/or clothes, etc. You can suspend your food up away from animals or drop items you wish to keep cold to the bottom of a lake, river etc. It also could serve as a fishing net, snare trap, etc…
Reminds me of the classic joke 
Two hikers are walking through the woods when one notices the other wearing running shoes. When questioned about it, he says that he wore them in case they meet up with a bear. His friend starts laughing and says, “Dude, YOU can’t outrun a bear.”
“Yeah I know, except I don’t need to outrun the bear”
Always take it, always use it.
Some other things:
Aluminium foil for camp fire cooking.
Cooking oil for frying. (This is one that I’ve genuinely thought “bugger!” when I’ve forgotten it and “great!” when I’ve remembered it.)
Rope
Mosquito repellant and mosquito bite ointment (essential if you’re camping with kids)
Like you say, it depends on the type of camping.
For us it’s usually about three nights at a commercial campsite.
Agreed. A mat or two is essential for me.
I tried that, but it turned out to also be self-deflating.
And that is a lesson I never do learn. 
I absolutely disagree. Even in mild weather the ground is a HUGE heat sink and can leave you chilly in a matter of minutes. The thermal insulation of proper ground pad is not something to dismiss lightly.
So burying rocks (from the campfire you shouldn’t build?
) and sleeping over them –which means waiting to pitch your tent until the rocks are hot, or not using a tent – is a better strategy than carrying a ground pad? Not in my book, and not for the vast majority of recreational campers I’d wager.
The use of a fire for cooking (or just building one at all) goes so far against modern low-impact/no-trace backpacking I can’t imagine doing it while in the backcountry. Now, if I’ve driven my car directly into a campsite then maybe I’ll build a fire in an existing ring, but I still don’t plan on cooking with it. A modern stove is just so much faster and easier than building a fire, waiting for it to burn to coals, and then worrying about making sure it’s dead out.
Buy a good poncho. The cheap ones don’t hold up well. A high-quality poncho will quickly pay for itself.
Most useful: Beer
Least useful: Wife, Kids, Dogs
Which gives me an idea for a very specific shop.
Poncho Villa.
flees
Helpful for car camping:
A good stove. Cooking over a fire, while part of the legendary romance of the outdoors, is often frustrating and sometimes impossible.
A good canopy – not the typical five-poles-and-guy-ropes dining fly, but something that’s easy to erect, won’t pool water in the rain, and stays up in the wind. Having a place to sit where the rain doesn’t fall or the sun doesn’t bear down can sometimes make the difference between reasonably pleasant and grudgingly miserable.
A lightweight folding table (example). Even if there’s a picnic table where you camp, this can be really handy. Can be placed where desired when desired, including under the canopy.
See my post #32 above on ground pads. A ground pad can be more important for warmth than a sleeping bag. The comfort helps a lot too for those not quite as hardy as Stranger.
A lamp for the table (eating, playing cards, etc.) that shines in one direction (see notes on lantern below.)
Dont bother:
A whiskbroom for the tent. Tedious to use and of limited effectiveness. Most any tent can be maneuvered to shake out whatever you want to sweep up.
A Coleman style lantern. Fuel powered ones are insanely bright, ruining any night vision. The 360º light illuminates things you’re not trying to see, and placed in the middle of a group simply blinds everyone.
THIS. Man, you only have to learn that lesson the hard way once for it to stay with you. Yeah, prepare for its being 20 degrees colder than the forecast. Carrying extra clothes if it’s hot beats the hell out of freezing when you’re several miles into the woods.
And put me on the pro-ground-pad side of that debate. The ground is an extremely effective energy sink.
I wouldn’t go without a sleeping pad, although I’ve never had any consideration for warmth. I went once without one, and I was up all night pondering the amazing force of gravity, and how although gravity is weak compared to the other forces, I could feel the entire Earth pulling me down. It seemed like the force of 500 pounds was being supported by the few pressure points in contact with the ground.
About the warmth, I never camp in the middle of winter, so I’m usually trying to find ways to keep cool. I won’t even go after mid-June. But I guess being in Texas, my concerns are not universal.
You most definitely want a sleeping pad (not an air mattress) – a very cheap blue foam sleeping pad from Walmart doesn’t provide much comfort but it will prevent you from being uncomfortably chilly. For under $100 at places like REI you can get a self-inflating pad that provides more comfort and more insulation, and if you want to spend more money, the inflatable pads can be even more comfortable, lighter, and take up less space in your pack.
My personal choice of sleeping pad, combining comfort, portability, at a reasonable price is the Klymit Static V Sleeping Pad
Forget the hatchet.
Forget the first aid kit – there will be plenty of those around in your situation. Maybe take a few band aids.
Minnesota in July = Ben’s 100% DEET. I’ve also heard good things about the OFF! Clip-on mosquito repellent but haven’t tried it myself. And some after-bite type of stuff.
Buy your shoes now and break them in. Hiking boots are out, trail runners are in – you want light weight, good traction, and stability, not several pounds of unnecessary weight on your feet.
If you are walking two miles to the campsite, I’d recommend determining if the trail is passable for a wagon. Walk in campsites are great, but carry the gear that far would be tough without transport. Costco has fold up wagons that can take a lot of weight, for like $40.
It depends on the demographics of the campers - Young kids? If so, then a lot of gear should be dedicated to their needs since if they are miserable then the adults will probably be too. My kids love glowsticks, flashlights, hammocks, stuff to throw in the fire 
Lots of good recommendations so far so I’ll mention some comfort items. I find a self inflating sleeping pad works pretty well, no need for a pump, and is pretty lightweight. A deck of cards and some poker chips goes a long way too A bluetooth mini speaker that can project from a device, and a big portable battery is nice. Good coffee. A good headlamp. If it’s cold, handwarmers inside the sleeping bag do wonders and they are super lightweight too.