Lotteries are one clear example where many people ignore the expected value of their cough investment -- although the case presented here may be an exception.

Anyway, a very other common form of lottery is called insurance. There, as well, your expected values is negative, still, most people do get (voluntarily, and sometimes involuntarily) insurances. If you had a million houses, it would make little sense to buy fire insurance for them.

I would argue that the expected value is too limited a criterion for rationality; we'd also have to include the subjective feelings of security (insurance) or possible fortunes (lotteries).