First Aid
A good first aid kit is absolutely crucial when going into the wilderness. Prebuilt kits sold at stores, which usually have some small bandages and pain killers, are a good starting point, but there are several other items that can help. A SAM splint is a moldable splint that can be used to splint a broken arm, wrist or leg. Carry cling wrap of some sort, as well as 2-inch tape, to secure a splint in place. Cling wrap and tape can also be used to to secure bigger bandages. Carry a 3-by-3-inch or 4-by-4-inch bandage for bigger wounds. A bandanna can double as a sling for an injured arm.
Signaling and Navigation
Carry a map and compass, or a GPS unit of some sort, for navigation, especially if you get lost. If you do get lost, it is often best to stay put to maximize chances of being found. A signaling mirror and a whistle can be used to call for help to rescuers who are nearby, especially if you are injured and can't move. Carry a headlamp or small flashlight as well for signaling at a distance. Carry matches in a waterproof container to build a fire, both for warmth and to help in being spotted.
Tools
A good multi-tool, like a Leatherman, is indispensable. These tools usually have saws that can be used to cut wood, pliers, knife blades and screwdrivers that can be used for gear repair. Bring a water filter or iodine tables to treat any water, because dehydration can severely exacerbate wilderness emergencies.
Carry a space blanket with you, even on day hikes or snowshoeing trips. These blankets are very thermally efficient and can help ward off hypothermia, especially when supplemented with a hat.