Part Two: Disclaimer.
As a Navy vet I've been through the standard USN ocean survival course, desert survival, and emergency preparedness training. Most Navy recruits are fairly close to becoming EMTs after they've completed basic training, and I could have gone to work as a Lifeguard if I'd wanted that career. However, I take my own advice and never rely on my own information alone when giving out advice. Some of my advice comes from military experience, some from FEMA, some from the Red Cross, and some from sources like "Cap'n Dave."
As a Los Angeles resident I've done my fair share of mountain climbing, spelunking, surfing, skating, geocaching, and camping. Again, I combine my own experiences with the wisdom of others before offering advice. The US Geological survey is always your friend; Get your maps, equipment lists, and skill requirements in that one site.
Part One: Advice.
This section is parsed into logically advancing difficulty from most common to least common likelihood of incidence.
Power Outage or Supply Blockage.
All most people need is a good source of clean water. In Urban and Inner city areas water isn't as easy to find unless you live near the reservoir or a stream. Here are some quick rules for survival.
Get two milk jugs, rinse them, and fill with water. Two jugs for each person in the home equals about four days of drinking water. These can be stored for more than a year, but I'd recommend refilling them once a year on New Years day or some other memorable occasion.
The average American home has enough food in it to last for more than a month. Leave the refrigerator closed for the first 8 hours. If the outage continues, then you want to begin consuming all the refrigerated food first, followed by all the frozen food. Refrigerated food that begins to warm will be bad within 24 hours or less, depending upon the food. Eat dairy and raw meats first (after cooking the meat of course.) Dispose of any food that goes bad in OUTSIDE trash receptacles. Don't eat when you are not hungry, just try to use up the perishables first.
DO NOT tamper with your water heater or fire hydrants, or any other utility such as power lines. Such activities could be fatal and are likely to be illegal. If the water has been off a long time, you'll want the water heater water for flushing the toilet. Don't drain it to drink out of, drain it into a bucket and use the bucket to fill the toilet reservoir. IF you have an outside source of "dirty" water such as a muddy stream or rusty water line, use THAT for flushing, and then you can drink from the water heater.
Ideally, you'll want to locate a source of fresh or filtered water, but most cities begin distributing bottled water by the second or third day anyway. Don't panic, just state your needs to the field workers. 90-some percent of all power and water outages are less than 4 hours in duration.
For the paranoid or the overachiever: Get a water filtration unit that you could use when camping. Stock a few crates of bottled water. A flat of ramen wouldn't hurt as a backup food source.
Earthquake, Hurricane, Tornado.
Damage caused by disasters can be more severe, lasting from a week to several months. The worst case on record is Hurricane Katrina. Here, again, the Government responds, and in force. Water, relocation, rescue, and other operations are typically enacted within 12-24 hours. The local government is usually incapacitated. State and Federal forces generally step in to provide service and safety.
Again, the thing you need most is water. Secondly, you need food. Tertially, you need toiletries. It's not impossible or expensive to stock up on these items yourself, and many homeowners do keep more than a month's supply of essentials (think of a 4 week camping trip) in the garage.
One other thing you'll need is to promote safety while at the same time being helpful. Rich people who distribute food are never raided or looted, it's the shopkeeper that people hate, or whom has lots of goodies in the window, that gets 'smashed and grabbed.' There's no reason to feel that you need to be armed or should fear the people around you. Humans are unusually cooperative and protective when disaster strikes. The media presents an image of looters and rioting that is far in excess of the realities of these situations.
Avoid touching any power lines or utilities. Do not scavenge or loot. ASK for help, loudly if necessary. Share resources that work, such as if your house still has power, water, or phone. Stay off the cell phones and home phones if there isn't a serious need to use them, as these facilities are often hard-hit, and emergency workers need the airwaves. Really.
Work with neighbors in small groups to obtain help, distribute whatever resources are gifted, and always listen to the service workers or national guard.
Government Failure, Anarchy, Revolution.
Think back to the Great Depression. Those circumstances were fairly dire for some people in some states. This is unlikely to ever happen again in our lifetimes, but even so it doesn't hurt to be prepared. A little paranoia won't hurt you.
Keep a small amount of gold or silver, or cheap gems in a house safe. These will help you survive temporary money-system failures with amazing ease. There are stories of widows auctioning jewels for food, etc. Be prepared for value systems to shift radically. Items that perish are less valuable than items that do not.
Don't bother to arm yourself more than you already are. Economic crashes rarely result in revolution or open fighting in the streets, and never since the French Revolution has this happened. The average household has enough items in it to create a respectable variety of weapons, if you think about it. I'll leave that topic to others more paranoid than I.
Generally, what happens is there is a bottoming out of valuation, followed by a graduated recovery. Severe economic damage only changes the level of activity. People don't stop buying and selling, but the prices change and the circumstances shift. You'll learn to be more thrifty and careful.
Drop all nonessential activities and spending. Eat cheaper, grow as much of your own food as possible, and cease entertainment activities like "shopping" and "nights out". You'll be fine. Ghana, Estonia, Bavaria, and a dozen other countries have been through exactly these circumstances and they're doing better year after year.
It's more important to pay attention to the local economy, people who need help, and building back a positive infrastructure.
Nuclear, Biological, and Chemical warfare.
In these cases, we're probably toast. Should you be lucky and survive, there are priorities, and you need to figure out what happened. A portable FM radio should provide needed emergency information. In the case of all three events, you're best-off if you stay indoors, if your shelter/home survived. The longer you can stay inside the better you'll fare.
If you travel outside, you'll face radiation, concentrated contamination areas, exposure to biologicals, as well as an increased risk of causing harm to yourself through accidents. Think about it. Thousands, or millions of other people will also stupidly be wandering about, looking for trouble, looting, assuming that the government is dead and all laws are void.
The government will not be dead. The ability of the government to protect you is probably dead, however. That doesn't mean that there won't still be national guard who'll shoot looters or defend federal buildings. Therefore, the best advice I can give is be prepared to remain indoors, quiet, and don't attract attention to yourself for the longest possible time.
Speak and interact only with uniformed people or people driving City or State or Federal vehicles. Going outside just to visit your neighbors could be the last thing you ever do if there is radiation, viral, or chemical pollution outside. Do what the radio tells you to do. This is absolutely positively the only time I'd advise anyone to trust the government. They're the ones who have to deal with the mess. Granted, Katrina wasn't a golden example of how to handle a disaster, but that's a specific example and a localized disaster complicated by levees, below sea-level lands, and other long-term problems which had never been addressed.