The Ten Essentials for Outdoor Activities

In the 1930s, a Seattle outdoors club called the Mountaineers came up with the original "ten essentials," a list of every item you need to survive in the great outdoors.

This list has since been refined into the Ten Essential Systems—which is more comprehensive, but doesn't quite have the same ring to it—and every outdoorsman has his own shortlist of "eleventh essential" candidates.

We make our Boy Scouts memorize this list pretty early on, and they each keep a small stuff-sack packed with their own 10E kit—kind of like a go-bag for camping.

All you need to add is a pack, sleeping kit (tent, sleeping bag, sleeping pad), camp stove, and change of clothes and you're good to go on any backwoods trip.

Combustion. It's wise to carry three sources of fire: lighters are easiest, but don't rely on them exclusively (and keep them in a plastic baggie to keep them dry); waterproof matches are handy (carry in waterproof container); a flint-and-steel type device is a good backup. Also bring along some tinder—dryer lint or a short length of frayable twine is good and easy.
Hydration. Bring at least a one liter water bottle (preferably two)—or a Camelback-style personal dromedary—as well as some method of filtering and/or sterilizing water from streams. For that, water pumps are reliable; chlorine tablets or iodine tablets are slow but effective; UV sterilizing wands are fast and nifty. The troop will always have a water filter or two on trips, but carrying our own iodine tablets is wise.
Nutrition. Always pack a bit more food than you technically need. The troop will provide food, but always have an emergency ration of your own (Granola bar, Powerbar, Snickers, GORP, whatever).
Navigation . - GPS. Bring your own compass. GPS units are fun, but always also have a topographical trail map and compass as they don't need batteries or satellite signals to work. And yes: it has to be an actual, physical topo map. (Note: Having the Trails.com app on your iPhone is not enough. Yes, Jon, I'm talking to you.)
Illumination - Flashlights are fine; headlamps are better (they leave your hands free). Bring spare batteries.
Tool and repair kit. A Swiss Army knifeor Leatherman-like multitool is essential. Needle and thread and dental floss (a super-strong thread substitute) are very handy. Wrap a few feet of duct tape around your hiking pole or a pencil for tent-pathing and pack-fixing.
First-Aid Kit. Self-explanatory. It's easiest to buy a pre-made hiker's kit from REI or any other camping supply store. The troop leaders will always have at least two first aid kits, but it's wise to carry a small one of your own. I always bring at least Band-Aids, pain relievers (including aspirin for potential heart issues), moleskin (for blisters), and Benadryl (for stings and other unexpected allergic reactions). Many argue that, these days, a cellphone is one of the most important items in your first aid kit so you can call for help if needed. Problem: much of the Great Outdoors is off the grid. (Mountaintops are best for catching stray signals.) I pack one just in case (but see the note below under "Communication").
Insulation. Bring an extra layer of clothing. I like silk long underwear (light and small—and comfy) plus a fleece top, a warm hat, and a lightweight rain jacket (which does double duty as an insulator and... well... as a rain jacket).
Emergency shelter - Space blankets are great and pack small. Even better to bring a poncho (doubles as rain gear).
Sun protection. Bring sunscreen, sunglasses, UPF lip balm, and a hat with an all-around brim. Long pants and sleeves count, too. Use them all.

... and the top candidates for 11th essentials:

Insect repellent. This is more of a comfort factor than a survival one (malarial areas aside), but bug spray and, if necessary, mosquito netting can make a buggy trip much less miserable.
Communication. It may seem antithetical to the backwoods ethos, but having a mode of communication—cellphone, two-way radio, sattelite phone for the isolated backcountry, even just an emergency whistle and a mirror or old CD (for signaling)—is an important survival tool. However, remember that scouts can only use their cellphones in emergencies—or to take pictures. No calling, texting, Internet, or games while on trips.
Preparation. Know what you're doing out there. Be well-trained. Also, for each trip, know where you are going and what your plans are. Feel free to ask your SPL for details and he'll be happy to share the information. The more people know what we're going and where we're going, the less time we waste milling around aimlessly.
Positive mental attitude. The best thing you can bring on any trip—and the key to survival in truly sticky situations.