Some great examples of unintended consequences from the Wikipedia listing for "Perverse Incentives":
1. In Hanoi, under French colonial rule, a program paying people a bounty for each rat pelt handed in was intended to exterminate rats. Instead, it led to the farming of rats.
2. 19th century palaeontologists traveling to China used to pay peasants for each fragment of dinosaur bone (dinosaur fossils) that they produced. They later discovered that the peasants dug up the bones and then smashed them into many pieces, greatly reducing their scientific value, to maximize their payments.
3. Opponents of the Endangered Species Act in the US argue that it may encourage preemptive habitat destruction by landowners who fear losing the use of their land because of the presence of an endangered species, known as "shoot, shovel, and shut up."
Update: Here's another example from one of James Gwartney's books:
4. In the former Soviet Union, managers and employees of glass plants were at one time rewarded according to the tons of sheet glass produced. Not surprisingly, most plants produced sheet glass so thick that one could hardly see through it. The rules were changed so that the managers were rewarded according to the square meters of glass produced. The results were predictable. Under the new rules, Soviet firms produced glass so thin that it was easily broken.
And here's another:
5. Private companies were paid to transport convicts/prisoners from the U.K. to Australia during the late 1700s and the early 1800s. The first payment schedule was based on the number of prisoners who boarded ships in the U.K. As you might imagine, there was no incentive to deliver living prisoners to Australia, and many of them died during the trip, due to overcrowding, lack of food and water, unsanitary and unsafe conditions, untreated diseases, etc. The payment schedule later changed, and was subsequently based on the number of living prisoners delivered to Australia. Result? Fewer prisoners died during transport.