Sleeping bag
More important than anything else you bring, a sleeping bag is essential to getting through the night. Temperatures will drop both outside and in your body, and a sleeping bag will provide warmth and comfort.
Camping tent
If you can be certain no rain or snow will befall your trip, in some extreme cases it's OK to travel without a tent. Most of the time, though, you'll want one with you. It provides another protective layer against the cold, wind and bugs, and it makes a world of difference when it rains. Special backpacking tents are built to be lightweight, reducing your workload.
Hiking Boots
As you add miles underfoot, you're going to get worn out--particularly on uneven or loose terrain--without hiking boots. They're not always the most comfortable footwear, but they will make it easier to get from Point A to Point B. Boots also provide support to your ankles, which can be under considerable strain when you're walking all day long with a 40- to 50-pound pack on your back.
Water purifier
You can purchase this at an outdoors store, and it's key to your health both during and after the trip. Microbes and other bacteria found in lakes, rivers and streams can come from unsavory points of origin, including animal fecal matter. If ingested, you can become extremely ill either on your trip or as much as two weeks after consuming the water. Water purifiers such as iodine will kill whatever is in the water and make it safe for consumption. Don't assume you can carry all the water you need on your back--each person needs at least one gallon a day, if not more.
Food
Don't ever rely on finding food as you go. Unless you're extremely experienced and know the land you're crossing well, you can't count on coming across anything. Pack more food than you think you'll need, and try to use foods that are compact and high in carbohydrates. If you are in territory where there are bears, pack your food in a bear canister to keep the scents from attracting any unwanted visitors.
Cooking stove
It's not essential if you bring dry-packed foods, but if you want a hot meal at the end of the day, a cooking stove can come in handy. Most are light, efficient and feature several hours' worth of burning.
Extra layers
Plan for unexpected cold weather--especially if you are going into the mountains. Bring multiple layers of pants, socks, underwear and shirts. Bring hats and gloves. You'll be happier carrying the extra weight than you would be if you get caught in a cold front and are forced to huddle up in your sleeping bag.