Shelter
It's pretty important to have some sort of shelter. Whether it be a tent, tarp, hammock, or simply a large poncho. It's always nice to sometimes sleep under the stars with no shelter or sleep in a snow hut, but you should always have some sort of shelter to fall back on. I even carry something that can double as a backup shelter such as tarp or poncho.
Sleep system
You always need some sort of sleeping bag or blanket. Even summer nights can get cold and it's always nice to have a little extra under you. It is vital that your sleep system is appropriate to the weather. You aren't going to use a 40 degree sleeping bag in freezing temperatures and probably don't want to use a -20 bag for summer. One of my previous posts will help you in determining your sleeping bag.
Water
Water is the most important thing in any hike. It's always better to have too much than not enough. I personally carry 2 Nalgene bottles. In the warm weather I also carry a camelback and a smaller aluminum bottle. Water does add a lot of weight, so it's important to also have some form to purify water if you go on any extended trip. I have a Cohglan water filter and purification tablets. In winter you can melt snow and don't really need a filter. Plan your trip well. If you know there's going to be plenty of water sources, carry less water and have a filter. If water will be scarce on the trail, carry more. I will post a bit later on how to find and carry water.
Food
Food is next to water in importance. Your food is all up to you. Your preference in food choices and the length of trip will determine how much and what kinds of food you will bring. There are dehydrated foods out there that you can just add water to. You can always get MREs or carry something like rice or noodles. Just remember that the more you bring, the heavier your pack will be. If you don't pack your food right, you will take up valuable space in your pack. I have been taking ramen noodles and rice in zip lock bags. I carry my food in a stuff sack, but a lot of people prefer to put each meal in its own zip lock bag. I like everything in the stuff sack because when I go to hang my bear bag, I just need to hang my one stuff sack. I will post some recipes for over the fire in a later post. If you bring things that need cooked, you need some type of stove, whether it be an alcohol, gas, or wood. You also need a cook set. I have a larger one for hiking with multiple people and for winter, and a smaller one for hiking alone. Bear in mind, you need something to melt snow in if you're hiking in winter.
Clothing
You should bring some kind of jacket along, no matter how warm it is outside. The nights may get chilly and you may get an unexpected rain. It's essential to bring extra socks. Depending on how hard you hike, the temperature, and weather, you may have to change socks during the day. When hiking hard in wet or hot weather, you should change your socks 1-2 times a day. Factor in additional clothing that has a potential to get wet or sweaty. It's also vital that you bring some type of hat. In the warm months, you need to keep the sun off your face and neck. In cold, you need to keep your head warm. Your head is very vascular, making most of your heat escaping through your head. When protecting from the rain, I recommend a small, spare poncho because you can keep the rain off as well as have a spare shelter.
Navigation
I prefer to use maps, I'm a little old fashioned but whether you use maps or GPS, you need something. You never know when you might lose track of where you are and may need to regain your bearings and get back on the trail. I carry a map in a waterproof map case, protractor, pencil, and orienteering compass. Not only should you have them, you should know how to use it. Take a small course or stay tuned for a later post I will put up on how to navigate. GPS is becoming very popular. If you bring GPS, make sure to have spare batteries or a way of charging it like a solar charger. In fact, you should have spare batteries for all electronics. You should also know how to use your GPS before setting out. If you do bring GPS, bring a map as well. You never know when the GPS will quit working or die and it's always good to have a map.
Pack
In my opinion, a backpack is important. I have never seen someone hike several days without one. The type and brand of pack you get 100% depends on what you like. I have a Teton sport explorer 4000. It's the right size for me and has plenty of room for all my gear. Every pack is different: some have lots of external pockets, some have none. There are several different sizes and styles. Do you want external or internal frame? Do you need some way to hold a water bladder? Do you want a built in pack cover or liner? Before spending a lot of money, determine what you need.
Tools
I highly recommend a multi tool like a letherman. These can be used for just about anything. I also like to carry a pocket knife. You should consider a small shovel to dig a latrine. I also have a folding saw to cut firewood and a collapsible snow shovel if I'm hiking in deep snow.
Light
I carry just a small LED flashlight. It fits into small places in my pack and is bright. I highly HIGHlY recommend a headlamp. If you end up setting up in the dark, it's nice to have a headlamp so you can work with both hands.
First aid
First aid kit is essential on the trail. Being how I'm a paramedic, I tend to go overboard with medical supplies. I recently condensed it down to the essentials: gauze pads, gauze rolls, alcohol pads, bandaids, moleskin, medical gloves, and antibiotic ointment. I also carry ibuprofen and Benadryl. Benadryl is great for allergic reactions. I carry my first aid supplies in a zip lock bag because it can compress more that way.
Everything else
Everything else you carry is based on your preference and type of hike. I will, later on, give you a guide on packing for winter trips, desert trips, and ultralight. The following are things you may want to also bring:
Lighter or fire striker
Some kind of tinder
Cord or rope (needed for bear bag)
Duct tape
Repair kits
Sleeping pad or air matress
Camera
Pillow
Space blanket
Survival kit
Gloves
Hand sanitizer
Backup stove
Bandanna
Carabiner
Fishing kit
Trekking poles
This will be a good start, but alter it to fit you. You may not use some stuff and you may have some stuff that you will use that I didn't mention. Feel free to comment about other things you carry.
