Here is an example of one called the Allais Paradox. It is presented by Jonah Lehrer in his blog The Frontal Cortex:
Suppose somebody offered you a choice between two different vacations. Vacation number one gives you a 50 percent chance of winning a three-week tour of England, France and Italy. Vacation number two offers you a one-week tour of England for sure.Go read the whole post to understand why we fall into this trap. You can also look at the Wikipedia entry for other details.
Not surprisingly, the vast majority of people (typically over 80 percent) prefer the one-week tour of England. We almost always choose certainty over risk, and are willing to trade two weeks of vacation for the guarantee of a one-week vacation. A sure thing just seems better than a gamble that might leave us with nothing. But how about this wager:
Vacation number one offers you a 5 percent chance of winning a three week tour of England, France and Italy. Vacation number two gives you a 10 percent chance of winning a one week tour of England.
In this case, most people choose the three-week trip. We figure both vacations are unlikely to happen, so we might as well go for broke on the grand European tour. (People act the same way with lotteries: we typically buy the ticket for the biggest possible prize, regardless of the odds.)