The point of the Ten Essentials list (developed by the Mountaineers Club, with origins in the climbing course taught by the Club since the 1930s) has always been to help answer two basic questions: First, can you respond positively to an accident or emergency? Second, can you safely spend a night or more out?
Most people including myself agree that the actually list has more then ten items on it. What I did is create my own list by combining some items together. Also keep in mind these items are only as good as your knowledge, skill and ability to use them. However if you have them or not, could mean the differences between life and death.
In a emergency situation regardless if your own survival or someone is hurt your ability to keep calm, keep a level head and use common sense will be critical to how things turn out.
Map and Compass (of the area your in)
Flashlight or Headlight with extra batteries
Extra Food (beyond what you plan to eat)
Extra Cloths (warmer clothing then what you have – say you had to spend the night)
Rain Gear (a $99 cent poncho is fine)
10 feet of Rope (para cord or ¼ diamon braid nylon should be fine)
Pocket Knife / Multi-Tool
Fire Starter (matches, lighter, flint and steel, etc all fine just keep dry and secure so they work when you need them)
Water (a way to treat water not a bad idea maybe a filter or chemical tablets)
First Aid Kit (a simple first aid kit should be fine)
Most lists include sun protection (sun screen, sun glasses and a hat) I don't include these as they won't save your life per say if your lost. Also you can use for example mud for some limited protection from the sun. I however do recommend you have sun protection, its just not part of my 10 list.
Some other good to have items include space blanket, toilet paper, duct tape, large trash bags (like the black yard ones), and a in case of emergency info card.