There are many types of coffee, but the most expensive and perhaps most exotic type of coffee is said to be an urban myth. It is said, that in Indonesia, a certain Civet cat eats the ripest coffee cherries straight off the tree. Knowing that this civet* would only choose the cherries that were best to eat, some daring men decided to sift through the feces of the animal to gather the beans. These beans came to be known as Kopi Luak or Kopi Luwak.
The kopi is not the most common cat in Indonesia, and finding the feces of a rare animal is hard. Given their scarcity and the daunting task of collecting the precious beans, the prices are (as can be expected) high. These beans are the most expensive beans produced, selling up to the astonishing rate of $200 (US). Markets in Japan, Italy, and the US have sprung up, and kopi luwak is seen more than ever before. Before you run to your local kopi luak dealer, you must realize that in the present Kopi Luwak has become somewhat of a marketing scam. It is estimated that 1 single bean in 2 tons of 'Kopi Luwak' coffee beans is actually true Kopi Luak. The rest of the 2 tons are produced in the same way as any other type of coffee.
{*}Thanks to Gritchka for the correction that kopi means coffee.