Map
Always carry a detailed map of the area in which you will be traveling. It should be a topographic map and you should know how to interpret the contours.
Many people carry a GPS. They are very useful for navigation, but one should not rely totally on such a device. It is not a substitute for a map.
There are two problems with a GPS. First, they are electronic and they can fail, e.g. the battery die. Second, the screens are usually small and only afford detail when zoomed-in and in this situation one cannot see much of the surrounding area.
Compass
Always carry a compass in the backcountry and know how to use it. You should know how to take a bearing either on the map or in the field, and how to convert to the other. This means that you need to understand the meaning of declination — the angular difference between true north and magnetic north. If all else goes wrong, you should be able to follow your compass back to a road.
Global Position System or GPS units, which make use of a satellite navigation system, have become smaller, more sophisticated and less expensive. More and more backcountry travelers are carrying them and they can help tremendously in navigating a difficult route. However, they are not a substitute for having and knowing how to read a topographic map and use a compass. The GPS may tell you in what direction your car is located, but it is poor for visualization of the terrain over a large expanse between you and your car.
Headlamp
Carry a headlamp, not a flashlight. Skiing in winter with a flashlight doesn't work well for the obvious reason — you can't hold it and use your poles at the same time. Be sure that that the batteries are good. LED headlamps use such small batteries that you can easily carry a spare set. Using the power settings prudently on multi-power headlamps can extend the life of the batteries. An added benefit of multi-bulb LED headlamps is that you don't need to carry a spare bulb and fumble in the cold swapping them out.
Food and Water
You should always carry sufficient food and water on your trip. You aren't carrying enough if each trip you return with no leftovers. Running low on either can result in loss of strength, coordination, warmth or judgment.
Extra Clothing
You should always carry sufficient clothes to cope with the expected conditions. You should also always carry additional clothes to cope with unexpected conditions and events. In the worse scenario you should be able to survive a bivouac.
You can minimize the weight of the clothes you carry by making sure that you can layer all your items. It's a waste of weight if you have to take off your pile jacket to put on your down jacket. And what good is a Gortex jacket if it doesn't fit over all your other clothes? The only justifiable "extra" clothes you should carry are gloves and maybe socks.
Highly recommended is adding a mylar bivy sack to your pack. It weighs little, is about the size of the cigarette pack, and can be a life-saving item if you are forced to bivouac.
Sunglasses and Sunscreen
The intensity of the sun in the mountains and on snow is much greater than elsewhere. There is less atmosphere to absorb the ultraviolet radiation, and both visible and ultra violet light reflect off the snow. Look for lenses that absorb both UVA and UVB radiation. For the best protection your glasses should also have side-guards.
Be sure to use a "broad spectrum" sunscreen with an SPF (sun protection factor) of at least 30. You should also use a lip cream that provides sun protection.
First Aid Kit
At a minimum you need a basic first aid kit with supplies to treat cuts, blisters and sprains, plus sunscreen. Add to it as you feel the trip requires. There are many good books and online references on first aid — what to carry and how to use it.
Pocket Knife and Tools
A pocket knife and duct tape are the minimum tool kit. The farther you go into the backcountry, the more additional items you should carry. Even on one-day trips it is common to carry epoxy, extra screws, a posit-drive screwdriver and even a spare binding cable. On multi-day trips it is common to carry a spare ski tip, a drill and bit.
Of course the best insurance against needing any tools is making sure that your equipment is in good condition before you head into the backcountry.
A note about screwdrivers. The screws used with ski bindings are not Phillips head; they are posit-drive. The combination of a posit-drive screw and driver allow for more torque to be applied to a screw.
Matches and Fire Starter
Carry matches that are both waterproof and windproof or carry wooden strike-anywhere matches and striker in a waterproof container. A commercial chemical fire starter can be useful in an emergency situation, especially if you are forced to "dig-in for the night." A magnesium block with striker is not a good choice for winter emergencies.
Signaling Device
Carry a signaling device such as a whistle.
Essentials 11, 12 and 13
Avalanche Beacon
There is no substitute for recognizing avalanche terrain and conditions. Although avoiding avalanche terrain and conditions is the safest choice one can make, you may choose to venture out when snow stability is less than optimum or cross a potentially avalanche slope. No piece of equipment can assure survival in an avalanche, however everyone in your group carrying an avalanche beacon adds another level of safety. Of course the beacons only help if they are turned on and everyone knows how to use them. Everyone also needs to have an avalanche probe and shovel.
Avalanche Probe
Time is of the essence when you are searching for a person burried by an avalanche. An avalanche beacon is the first tool used to locate a person. An avalanche probe is then necessary to locate the exact position before beginning to dig. Not using a probe wastes valuable time that can be the difference between life and death.
Snow Shovel
Everyone should be carrying a snow shovel if they are carrying an avalanche beacon and probe. Locating a buried victim does little good if you don't have shovels to dig them out quickly.