10 Essentials

According to the eighth edition of "Mountaineering: The Freedom of the Hills" (2010) book there are ten essentials. They were given as a guideline, where you needed the group to have each of these areas covered. Not each person needs all 10 of these, but there should be a little redundancy in case the group splits into smaller teams or gets isolated.

Navigation. Topographic map and assorted maps in waterproof container plus a magnetic compass, optional altimeter or GPS receiver.
Sun protection. Sunglasses, sunscreen for lips and skin, hat, clothing for sun protection.
Insulation. Jacket, hat, gloves, rain shell, and thermal underwear.
Illumination. Headlamp, flashlight, batteries. LED bulb is preferred to extend battery life.
First-aid supplies, plus insect repellent.
Fire. Butane lighter, matches in waterproof container.
Repair kit and tools. Knives, multi-tool, scissors, pliers, screwdriver, trowel/shovel, duct tape, cable ties.
Nutrition. Add extra food for one additional day (for emergency). Dry food is preferred to save weight and usually needs water.
Hydration. Add extra 2 liters of water for one additional day (for emergency). Portable water purification is also recommended.
Emergency shelter. Tarp, bivouac sack, space blanket, plastic tube tent, jumbo trash bags, insulated sleeping pad.

The book also recommends adding extra equipment to handle your specific terrain, as well as signaling devices. They could include a whistle, mobile phone, two-way radio, satellite phone, unbreakable signal mirror or flare, laser pointer, or any items that could contact potential sources of assistance