The economists' way of thinking often leads to surprising results. One famous meme concerns the impact of seatbelts. At first blush, it appears obvious that wearing a seatbelt reduces the harm caused by an accident. The economist pipes up saying that it also increases the probability of an accident because the person feels safer; it probably increases the severity of the accident as well. While at an engineering level, seatbelts are of course wonderful, the overall effect is more cloudy than is commonly believed (link). You would need to study the data; it isn't obvious that seatbelts help. And if the adverse impact upon driving were bad enough, the economist would argue that a spear implanted in the steering wheel, pointing at the driver's heart, would probably do more for the health of the public than seat belts.
A similar debate surrounds the impact of motorcycle helmets. The biologist knows that a skull encased in a helmet does better when exposed to an accident. The economist worries that the probability of an accident goes up when the mind feels protected in a skull that's encased in a helmet. The two effects run in opposite directions; you'd need to study the evidence to know which one dominates.
Laymen often find `moral hazard' arguments to be downright bizarre. Do you believe that people actually take less care of their own health when covered by health insurance? Do you believe that people slack off in a job more when there is unemployment insurance or when it's hard for the employer to sack 'em? Do you believe that young people growing up in a welfare state invest less in human capital and have an inferior work ethic? Do you actually believe that the rise of the European welfare state had something to do with the breakdown of the family as an institution in Europe? These kinds of propositions almost sound morally repugnant. I think such behavioural changes do take place; people do respond to incentives much more than meets the eye.
Today I saw an amazing and new variation on this theme in the New York Times: cyclists who wear helmets are more likely to get hit by the traffic.