Buying extended warranties is foolish, as this Washington Post article clearly shows.
"The things make no rational sense," Harvard economist David Cutler said. "The implied probability that [a product] will break has to be substantially greater than the risk that you can't afford to fix it or replace it. If you're buying a $400 item, for the overwhelming number of consumers that level of spending is not a risk you need to insure under any circumstances."
Since extended warranties don't typicallly cover wear and tear damage -- the main reason consumer goods fail -- you would basically be buying insurance that covered an extremely unlikely event, that a product would suddenly become a lemon after the manufacturer's warranty lapsed. At the point an extended warranty kicks in, you'd generally be better off replacing whatever item it is with the up-to-date model rather than having a third-party repairman of the insurance company's choosing fix an outdated piece of electronics, probably at great inconvenience to you. You would do better putting that extended warranty money into a slot machine and setting aside whatever money resulted in a repair/replacement kitty.
Behavioral economists point to extended warranty purchases as an example of irrational risk sensitivity, but it seems to me like more a case of asymmetrical information. Spending makes consumers feel vulnerable, and retailers exploit that discomfort buy selling them an insurance product they know their customers don't really need. Customers buy a sense of well-being that evaporates, probably the minute they walk away from the register, away from the salesperson's nagging predictions of doom. (A variant on this is the pernicious practice of rental-car agents forcing unnecessary insurance on customers in an even more confusing retail and regulatory environment, typically conjuring up doomsday scenarios and implying legal ramifications for customers that are dubious to say the least.) You end up with the feeling that the company hopes the product it just sold you will break, to spite you for rejecting their warranty -- which is where it makes its money.
For what's startling, and what helps explain their popularity, is this fact, also highlighted by Tyler Cowen in this Marginal Revolution post: "Neither Circuit City nor Best Buy discloses how much of its bottom line comes from extended warranty sales. But analysts have estimated that at least 50 percent and in some lean years 100 percent of profits at the electronics retailers come from extended warranty sales." No wonder the salespeople are so pushy.