There are many reasons why the power goes out. Electricity can be knocked out by just about any natural event, lightning, storms, tornados, hurricanes, floods, fires, earthquakes, snow, ice, the list is virtually endless and wherever you live, one or more of these probably effect you.
You are more likely to be affected by natural disasters if your power lines are above ground. Trees seem to be attracted to them and often fall onto power lines. Ice can build up on them causing them to snap under the weight, or ice on the trees can cause them to fall on the power lines. This is particularly bad because that means it is cold outside and even people with gas heat need electricity to run the fan that circulates air. In the summer, lightning storms may be common in your area. lightning strikes or high winds often knock down trees onto the power lines. If there is a bad storm, it may take a while before they get to your area. Where I live (Maryland, outside of DC) every summer there is at least one storm that knocks out power to an unlucky few for a day or more.
There are also man-made reason the power goes out, someone could hit a utility pole, a Mylar balloon could short out a transformer (don't laugh, I've seen it happen), or the power company could just not have enough during peak demand. When the power company doesn't have enough electricity to go around, you either get 'brownouts' where they lower the voltage to everyone or rolling blackouts where the power company intentionally cuts power to different neighborhoods, generally for short periods of time to spread the pain. Usually peak demand happens in the summer between noon and eight PM when everyone has their AC running, but this winter (2000/2001) California has been having problems getting enough electricity on winter nights.
Electricity demand has been steadily increasing and the number of power plants hasn't kept up. This isn't likely to change in the next few years, so brownouts and blackouts are likely to become more prevalent. They primarily effect the east coast and the west coast, where the population is heaviest.
The good news is that America's power grid is very reliable. About 99%. That sounds good, and it is, but since there are 8760 hours in a typical year, if the power is out 1% of the time that is 87 hours without power! More than Three Days! Hopefully that won't come all at once. Of course, most years you will have even better reliability than that, I generally loose power for 8 to 10 hours a year and usually during the summer, but I try to stay prepared for 2 or 3 days without power.
Critical to preparation is determining the most likely time of the year power will go out, how long it will stay out, and what the cause might be. Start with your own experience, if you haven't lived where you do long, ask some neighbors. Keep in mind that different parts of the same city may have different rates of failure. Finally, think about where you live and what kinds of power failures are likely. If you live in the southeast, hurricanes and thunderstorms are common, in the north, particularly the plains and New England, Snow storms will be a problem. In California, you have to take earthquakes into account.
Winter power failures cause particular hardship because you won't have heat. If you live in an area that doesn't get much snow or ice, keep in mind that if the power goes out, the roads might not be in any condition for you to drive on, even the power company may have trouble getting to where the problem is.
Earthquake prone areas require special care. In the event of a quake, you don't want to go lighting candles until you are sure there are no gas leaks in the area.
The frequency of power failures impacts your planning. If the power goes out for an hour or so once or twice a year, you don't need much more than a couple of flashlights. If however, it goes out once a month for half the day, you may want to go all the way and get a generator. Only you can decide your tolerance for these interruptions. Since most of the supplies I recommend are inexpensive, I think it is better to be safe than sorry. Also, you don't have to get it all at once, you can build up your supply over several months.