There are many many variables that interact which can affect an individual's survival in a number of disasters or events. This is in no means an attempt to be comprehensive, and it is important to know that the priorities of these things may vary a bit depending on the situation.
(http://www.survivaljoe.net/top-10-survival-skills-for-kids/)
First off, it is important to remember that the most important tool anyone has in their survival toolbox is their brain. Keeping calm and drawing upon the knowledge we have undertaken to learn is crucial to survival. Panic is the enemy. Even if we face a situation that we have not studied or become familiar with, a calm mind can often piece together a solution from the things we do know. Never stop learning, and committing techniques and skills to memory through practice. As an example, I have trained my kids in fire building with different techniques until they are as good or better than I. And I've done this through competition as they get older, thus challenging myself to remain skilled.
But the rule of 3's gives us a handy way to think of essentials when life is at stake.
3 Minutes
In general a person loses consciousness after about 3 minutes without oxygen. Obviously, there are freedivers and others who have trained their cardiovascular systems to amazing lengths of holding one's breath... but these are general principles. The types of scenerios that cause oxygen deprivation are hard to plan against, and usually are a panic, so training may have minimal value. Being trapped in a fire or airtight material/container, drowning, carbon monoxide poisoning, choking, etc... are all intense, rapid onset situations and other than escape, there is little that can be done to change these events. However, knowing this "3" is handy because it helps responders know how to react. Amazing things have been seen with children drowning in icy water, which seems to slow metabolism and reduce the damage caused to brain cells from oxygen deprivation, but in general, speed is of the essence if someone is not breathing, and after 3 minutes, expect failing consciousness... after 10 minutes... permanent brain damage is very possible.
3 Hours
Exposure can cause severe compromise to our bodies and greatly affect our ability to continue surviving. Severe heat without water or protection from the sun can cause Heat Stroke, and likewise severe cold without protection from wet and wind can cause hypothermia leading to frostbite. Even though people often will live much longer than 3 hours in these adverse conditions, their competency to perform survival related tasks can be hindered. Proper preparation before heading into potentially dangerous elements... If one faces potential heat... sun protection for skin and assuring plenty of water are key. For cold environments, layered clothing that protect against moisture (both from elements and from sweat accumulating against skin while working) are key. Further, learning skills and having tools to build a fire is essential. A person might be appropriately dressed for a winter hike, and then slip into a stream, suddenly to find themselves in danger of hypothermia. Simple preparations carried with you add little to your hiking weight, and can be a life saver for you or a hiking companion. We'll talk more about gear next time.
3 Days
In general, we have lost great functionality and can be rapidly facing death after 3 days without water. This one is probably the biggest and most important need for the largest varieties of personal disasters. This situation doesn't just affect the adventurer in the outdoors or the victim of a point in time event such as choking or drowning. People can find themselves without water any time the power is out locally, where public utilities are down. This can affect them after storms or other natural disasters. It also applies to those who are out in the wilderness, finding themselves out of the potable water they carried. Progressive dehydration will lead to altered cognition and an inability to think and act clearly, worsening the problem. 
This outlines both pre-filtering water and then purifying it for infectious agents. There are some other tools that can be used that I want to outline later, but this is a fantastic post regarding preparation for water issues.
(http://renalfellow.blogspot.com/2009/04/how-to-do-water-deprivation-test.html)
3 Weeks
While people have lived a lot longer than 3 weeks, we find most people used to normal meal times will find themselves physically and mentally challenged by 3 weeks of drastically reduced diets. This situation is often heightened in a disaster situation since these events typically increase our activity. Foraging for food, water, wood, etc... can burn a lot of calories, which further hastens our decline. Preparing for dietary needs during our hiking, camping, and even as a reserve at home for an unplanned situation is essential.
(http://spaceonwhite.com/true-flavor-retained-survival-food/)
Part of being aware of these needs is for self-preservation, but it is also crucial, once one has reached that first stage where we have become somewhat knowledgeable and competent in survival that we are planning to help our neighbor. While we might know and master the basics, know how to build a fire with wet wood, know how and have preparations for clean water and emergency food... we must realize how many people have no idea how to take care of themselves and their families in a dire situation.