7:03 p.m. on August 8, 2012 (EDT)
First you have to provide for the survival essentials.
Let's start with the zero essential - something you actually leave at home instead of taking with you: detail information about your plans, including expected return or return contact time, left with a trusted relative or friend who WILL call the appropriate authorities if your don't return or make contact as expected. Here is an epic failure you'll often read about: "the search didn't start until Tuesday when fellow workers became concerned about the hikers missing 2 straight days of work...."
Next are the other survival essentials, but instead of a shopping list, think about your needs and the equipment that will provide for them. In that context, the rule of threes is a good start: You can survive 3 hours without protection from the elements, 3 days without water, and 3 weeks without food. But you can't survive much more than 3 minutes without hope.
Providing for the zero essential gives you hope that even if you become lost or unable to return as expected there will be an SAR out looking for you. Providing for the remaining essentials gives you hope that'll you'll be able to survive until you are found.
So that takes care of the big two.
You need adequate protection from the elements, be it cold, heat, sun, or rain. That means appropriate clothing and shelter for the expected conditions, sch as a set of dry clothing in case what you are wearing gets wet, adverse weather protection - rain gear, snow gear, sun screen, etc., sleeping bag, and a tent, tarp or hammock (if you don't expect rain a good poncho can provide both protection from unexpected rain, and shelter in case of rain.)
You'll need a whistle for signaling. 3 short blasts is the international signal for distress. It's surprising how much further the sound of a whistle will travel over the sound of your voice.
A flashlight or headlamp, and sufficient batteries (in addition to the ones in the flashlight or headlamp) will help you avoid injury while exiting in low daylight or having to carry out other survival activities if needed at night.
You'll may need a way of starting a fire, for warmth or signaling. Usually not absolutely necessary, but a fire often gives comfort to people who are awaiting rescue.
You must also protect yourself from injury and illness from the elements, so you'll also need a first aid kit.
You don't need food and water to survive, but without adequate hydration and energy you might suffer illness or inability to protect yourself from the elements. Unless you will carry enough water for 2 or 3 days (highly unlikely) you need a means of collecting water and purifying it. You could just boil if you bring a stove and sufficient fuel. Or you get a filter and purifier system to reduce the amount of fuel you would have to otherwise carry.
Check on the net for the likely amount of caloric intake per day needed for your weight and expected physical exertion. Take at least one more day's worth of food that you think you'll need.
Remember that you need to replace electrolytes when drinking lots of water. That means sodium, potassium, and chloride at a minimum. Foods with minerals like zinc and magnesium are also helpful.
What you don't need to survive is a map and compass. But both, and the ability to use them, can help you avoid getting lost in the first place and thereby avoid having to call on all the other essentials equipment you have assembled. If you know where you are then you are not lost. a map and compass help you keep from getting lost. A gps can do the same thing and more, but even though I hike explore mostly by gps, I still carry a map and compass as a backup.
Now you can take a look a the so-called "ten essentials" to fill in the rest of your shopping list.