While animals do not cry in the way that humans do, they do produce tears. Since tear production, called lachrimation, is necessary for healthy eyes, most vertebrates are capable of producing tears.
Tears are produced in mammals by the lachrymal system, tissues which make water. In land mammals, tears evolved to replace the water bath that the eyes of aquatic animals and fish are constantly surrounded by. Tears serve to clean the cornea and keep it moist. When a speck of dirt, for example, is lodged in the eye, more tears are produced in order to wash away the irritant.
The fluid in tears is rich in nutrients and has anti-bacterial properties which help to fight infections. The salt in tears helps to create an osmotic balance within the eye.
In animals, it is virtually impossible to tell if their tears are the result of emotions or merely caused by eye irritation. Most scientists agree, however, that humans are the only animals who produce emotional tears.
While animals may not weep like humans, they do, however, emit cries which seem to indicate emotional distress. Baby animals of all kinds will vocalize when separated from their mothers. Baby elephants in particular produce a very sad, keening sound which sounds like weeping. Hunters and some wildlife experts have claimed that the sound of a bear cub cries, when separated from its mother is remarkably similar to the cries of a human baby. In these cases, the cries probably serve as a form of direct communication with the mother.
There are many cases of animals exhibiting grief at the death of their owners. The famous Greyfriars Bobby, a small dog whose owner passed away, kept constant watch over the grave until his own death fourteen years later. A statue and fountain were later erected in honor of the faithful terrier.
Ascribing "human" emotions to animals (anthropomorphism) is often derided but may have a factual basis. A poodle which has lost a canine companion may refuse to eat. Dolphins have been known to carry their dead babies with them for days. An elk may stand watch over the dead body of a calf until predators destroy it and geese mate for life. While it is virtually impossible for a human to know what animals are really thinking or feeling, these behaviors seem to indicate real emotions.
Elephants, which are sensitive and highly intelligent animals with an evolved social structure, have been observed "crying." Charles Darwin was told by the keepers of Indian elephants at the London zoo that the animals shed tears from sorrow.