First, keep your thoughts with the people of Japan. From what I can tell, their government has responded very well to the emergency, and as bad as it appears to be, it could have been much worse.
Second, while I'm a serious tightwad, there are limits beyond which are just plain stupid if you have a choice. I'm thinking about people who refuse to evacuate in the face of current or possible natural disaster. Yes, many times, the actual result isn't QUITE as bad, but the warning was issued because there was the significant probability it could be. That's because scientists know that when A happens and B happens and you have C circumstance, you have the ingredients for D to happen, and X percent chance that it will be in this range of severity. You will almost never get a scientist to tell you that there is 100% chance of an outcome. Even if you do something phenominally stupid and normally fatal, a scientist would still probably hedge that bet to a little less than 100%. Why? Because the rope could break, something might break your fall, etc.
We in the US have a marvelous system of warnings from the USGS and the NWS. So don't be the moron who ignores the warning, or worse, who goes out to WATCH. The people who ignore hurricane warnings are the ones who baffle me the most. True, some people legitimately don't have the resources to truly evacuate, but most people do. It's always the people who refused to evacuate because "it won't be that bad" or they're afraid of looting who end up frantically calling for help in the middle of the hurricane, expecting other people to put themselves at serious risk. I'm of the rather cold-hearted opinion that anyone who refuses to listen to a warning should have to wait until the rescuers aren't at significant risk themselves, but I know several people who do this sort of work. If there is any possibility of reaching the people, they'll try. And a year later, the same people who were rescued will be campaigning to cut salaries or something else for those same rescuers.
So, the limits of frugality? People matter much more than things. Staying because of "looters?" Really? You want to risk your life, your family's lives, and all the people you potentially put at risk trying to help you, for a few possessions? I won't even get into the fact that you're more likely to arm the looters than actually hold them off.
I'm old enough to remember Mt. St. Helens going up, and there were a few people who refused to evacuate. I still hear some people talk about how terrible that was. In my view, they chose to commit suicide. However, I still feel for the family who were outside what was supposed to be the high risk area (if I recall the details correctly), a reminder that the scientists give us what they think is the worst SIGNIFICANT risk and they had more limited experience in predicting the effected area. Unfortunately, it was even worse than they predicted (something to keep firmly in mind). I also consider the USGS vulcanologists who've been killed in their attempts to investigate and understand volcanic eruptions heroic.
My point is, don't be stupid. You cost yourself and others, possibly paying in lives. If you have to risk your own life, then go do it through something pointless like bungee jumping that doesn't risk anyone else.