One area we aren't always too careful about is preparing for something as minor as a power outages. Frugal people often have a month or two worth of food stored and tend to feel well-prepared because of that, but forget to look at WHAT food they have stored.
If we lost power during the summer, our apartment would be almost unliveable without AC during the day. There are few windows or trees and our normal summer highs are in the upper 90s. If we had power, we could run a couple of fans to keep the temperature bearable, but if the power was out, it would quickly rise to well over 100F. In the winter, however, we rarely have lows below freezing, and we could get by with dressing warmly, pulling out the winter sleeping bags to add to the beds, and keeping faucets dripping to avoid frozen pipes.
Water is usually less of a concern. We keep several gallons of water in the house, and if we knew a hurricane was possibly heading for us (the likeliest major natural disaster for us), we'd put several large storage tubs in the bathtub (doubled in case of leaks) and fill them with water for washing, then fill every possible pot and container in the kitchen for drinking. The toilet would get flushed with wash and dish water. My estimate is that we'd get by for at least 2 weeks.
We have half a dozen flashlights, two battery lanterns, and a number of batteries of all sizes, including rechargeable AAs and AAAs that we check regularly for charges.
The one thing we're guilty of is looking at the cabinets and thinking we have plenty of food to eat. The problem is, most of it is food that requires a lot of cooking time, and we have an electric stove. And some other foods aren't very edible without being warmed at least a little. Some people have grills or fireplaces or camp stoves, but don't always think about the fuel for these in advance.
With this in mind, we store several boxes of saltine-type crackers, granola bars, nuts, cans of mini-hot dogs, cans of fruit, and some things like soup that just need to be heated a little. At any time, we also have cheese, fruit, tortillas, bread, and peanut butter that don't necessarily have to be refrigerated, plus a couple of packages of hotdogs that only need minimum heating. Those things can be moved into the cooler with some ice to keep them fresh as long as possible.
We don't currently have a grill or camp stove, which is something I'm keeping an eye out for. What we do have are candles. With extreme caution, you can use a candle to do some minimal cooking. One way to do it is simply "toast" bread over the flame and "roast" hot dogs or the canned mini-hot dogs.
A second method requires a tea candle, a clean, empty tomato sauce can, and a small metal cup or camping pot. Poke a hole or two in the can for air using the pointed end of a bottle opener and remove the label. Light the tea candle, put the open end of the can over it, then set the metal cup or pot on top of the can (make sure it's stable for safety). You now have a means to warm soup and other foods. I'm not sure you could get it hot enough to make coffee or tea, but it might be worth trying. WARNING: Be very careful with open flames to avoid catching anything on fire. Handle the can and the cooking cup/pot. Remember, the tomato sauce can will get VERY hot.
There are other variations on this, of course; refer to camping sources. In the girl scouts, we used to make buddy burners, but those seem like a lot of mess to me.
I'd love to hear from other people on their frugal ideas for storing foods that don't need cooking, or need very little...