While animals do not crycrycry in the way that humans do, they do produce 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.
http://www.wisegeek.com/do-animals-cry.htm