Most of the 5,400 mammal species are covered with enough hair that it is thick enough to be called "fur" — both marsupials and placentals are usually covered with a conspicuous layer of fur, which helps keep them warm. Obvious examples are kangaroos, mice, bears, cats, and dogs.
Some mammals have hair so short, that when you look at them from a distance, it isn't noticeable. Only when you look at them close is it apparent that these are just mammals with very short hair. Examples of mammals with very short hair include elephants, rhinoceroses, cetaceans (whales and relatives), the naked mole rat, and us humans. In particular, humans being among the mammals with very short hair has caused no small amount of controversy, with some creationists claiming that the human absence of long hair is evidence that we were created by God as a fundamentally different entity than the rest of the animal kingdom.
Even to evolutionary biologists, the reasons why hair gets so short that it practically disappears are unclear and a subject of much controversy. For marine mammals, like whales, the reason seems clearer — to be streamlined for swimming. The naked mole rat is one of the mammals with very short hair because of its underground lifestyle. Although the naked mole rat does have a few long hairs for sensory purposes, most of its skin is relatively hairless, giving it the name "naked."
The most controversial of the mammals with very short hair is, of course, the humans. Why did humans lose most of their hair a million years ago or so? Currently, no one knows. Some scientists believe that early members of the genus Homo, from which humans evolved, spent so much time in the water that they evolved various adaptations for a semi-aquatic lifestyle, including short hair and increased subcutaneous fat. Others believe that it had something to do with the regulation of sweating. Overall, more research and theorizing is needed.