The 10 Essentials were developed by The Mountaineers in 1930 as a guide for hikers. In 2003 they updated their list to a newer 10 "systems". The 10 systems are:

Navigation
Sun protection
Insulation
Illumination
First-aid supplies
Fire
Repair kit and tools
Nutrition
Hydration
Emergency shelter

It is a good habit to bring these whenever you go hiking or camping for any length of time.

Step 1: Navigation

A navigation system should include at least a map and compass. You could also include a GPS and/or an altimeter.

Your Map should be a topographic map, current, and of the area, you plan to visit. You should also know how to read it.

Step 2: Sun Protection

Sun protection is especially important in the summer and the winter. Sunscreen should be at least SPF 15 but higher is better. It should also block both UVA & UVB rays.

Step 3: Insulation

Insulation is largely dependent on the weather. But you should always include an extra pair of socks. If it looks like it will be cold then you would want to include gloves, coat, extra shirt, etc. Bring items according to what the weather looks like.

One item I have found very useful is shemagh. It's very warm and it works well as sun protection. As well as many other things. I am planning on writing an Instructable on it later.

Step 4: Illumination

Flashlights are a major part of the illumination system and typically they are more powerful than headlights. Headlights are easier to use though, as they don't require you to hold them. Always bring extra batteries along as you don't want to be without light. Also, you could include a chem light they glow for quite a while.

Step 5: First-aid Supplies

I don't have a background in medicine so take my advice with a grain of salt and check out what others say, but I carry:

Medical Gloves
Gauze Pads
Roller Bandage
1st aid tape
Alcoholic Prep Pads
Band-aids
Antibiotic Ointment
Moleskins
Super Glue
a Needle
a CPR Mask

Again don't carry anything you don't know how to use.

Step 6: Fire

The five main fire starting methods are:

Matches- best idea is waterproof with a case, tinder, and strikers
Lighter- you can get a gas or an electric version
Flint and Steel- this takes some skill and practice
Friction- this also can be challenging one example is the bow drill
Magnification- this takes the sun, skill, and a way to magnify the sun (magnifying glass, clear water bottle)

Whatever method you use make sure you know how to start a fire using it also it would be a good idea to bring multiple ways to start a fire and extra tinder

Step 7: Repair Kit and Tools

The tools you bring and your repair kit will depend on what you pack. If you bring a tent then you probably need a repair kit for that. Some items to include in your repair kit are duct tape (fixes everything) needle and thread (for tears in clothing, backpacks, tents, etc.).

The main tools are knives and Multi-tools. A multi-tool should be simple and robust. You can find a more detailed buying guide here.

Step 8: Nutrition

Always pack a day's worth of food. Freeze-dried food can be good but no-cook food items are also good to bring as you can eat them on the trail. Just don't leave any around for animals.

Step 9: Hydration

Water is one of the most important things to have and you should bring more than you think you need. It is a good idea to get a method of purification such as a life straw. A metal water bottle is a good idea as you can boil water in it.

Step 10: Emergency Shelter

Emergency shelter is more for if you are day tripping and you aren't bringing a tent. But you could still bring some shelter even if you have a tent (in case your tent gets lost). Emergency shelter can include a tarp, tube tent, space blanket, or bivy sack. Whatever you bring, make sure it will keep you warm.