1. Knowledge. What good is a compass if you don't know how to use it? Play with matches if your fire-making skills are shaky. Learn what to do when you see a bear. Read a little, practice a little - knowledge is more likely to save you than gadgets.
2. Map and compass. These are together, because that's the way you need to use them.
3. Matches and lighter. Bring both, or waterproof matches and a fire starter of some sort. Having two ways to start a fire is much safer.
4. First aid kit. Buy a pre-packaged one or build your own. Make sure it has pain relievers, bandages, disinfectant, and notes on basic first aid procedures.
5. Foot care. Your first aid kit needs moleskin, and maybe a pin, to treat blisters. Your feet have to be well cared for when you're hiking miles from the nearest road.
6. Water purification. A filter works, but they clog and break so often that you should have a small bottle of iodine tablets or other water purification as back up.
7. Rainwear. One of the biggest killers in the woods is hypothermia, and it often starts when you get wet. Try to stay dry.
8. Shelter. This can be a tent, tarp or bivy sack. Just be sure you know how to use it.
9. Sleeping bag. Down bags are the warmest for their weight, but be sure you know how to keep it dry, or bring a synthetic bag.
10. Specific trip items. For backpacking trips in Michigan in May, bring insect repellant. In June in Arizona, bring sunblock. Think about the specific conditions for the time and place of your trip.
Make your own list if you take regular backpacking trips. It's no fun when a friend tells us ten miles down the trail that he's allergic to bees and forgot his medicine. A little planning means less worries, and a better trip.
