Map. A map not only tells you where you are and how far you have to go, it can help you find campsites, water, and an emergency exit route in case of an accident.
Compass. A compass can help you find your way through unfamiliar terrain—especially in bad weather where you can't see the landmarks.
Water and a way to purify it. Without enough water, your body's muscles and organs simply can't perform as well: You'll be susceptible to hypothermia and altitude sickness. not to mention the abject misery of raging thirst.
Extra Food. Any number of things could keep you out longer than expected: a lengthy detour, getting lost, an injury, difficult terrain. A few ounces of extra food will help keep up energy and morale.
Rain Gear and extra clothing. Because the weatherman is not always right. Especially above treeline, bring along extra layers. Two rules: Avoid cotton (it keeps moisture close to your skin), and always carry a hat.
Firestarter and matches. The warmth of a fire and a hot drink can help prevent an encounter with hypothermia. And fires are a great way to signal for help if you get lost.
First aid kit. Prepackaged first aid kits are available at most chemists. Double your effectiveness with knowledge: Take a basic first aid class, offered by many organizations.
Army knife or multi-purpose tool. These enable you to cut strips of cloth into bandages, remove splinters, fix broken eyeglasses, and perform a whole host of repairs on malfunctioning gear—not to mention cut cheese and open cans.
Flashlight and extra bulbs. For finding your way in the dark and signaling for help.
Sun screen and sun glasses. Especially above treeline when there is a skin-scorching combination of sun and snow, you'll need sunglasses to prevent snowblindness, and sunscreen to prevent sunburn.