Mammals are defined as being warm-blooded, air breathing vertebrates with hair or fur and the ability to nurse their young, notes the San Diego Zoo website; humans and some bat species are examples of mammals without visible tails. While most mammals do have tails that feature is not a determining factor in their classification as mammals.
There are more than 4,000 species of mammals. Tails function in many ways. Some tails are used to swat away flies, to keep balance, to ward off predators, to grab things, to keep warm and to store fat. White-tailed deer flash the underside of their tails to convey danger. A dogs' wagging tail or tail between the legs conveys emotion. Sea mammals use their tails to navigate through water and some monkey use their prehensile tails as an additional appendage.
Some mammals that are without tails include the hog-nosed bat and humans. In mammals, a tail is the part of the body that corresponds to the sacrum and coccyx. Mammals without visible tails, like humans, do have a coccyx referred to as a tailbone that does not protrude externally. A human embryo does have a tail but is absorbed into the fetus during gestation.