Assuming you're only referring to tears as an emotional response, then the answer is no; only humans shed tears to convey emotion (at least, no scientific paper has been written to prove otherwise). If you're referring to the shedding of tears more generally, then yes; many land animals do this! Tears are extremely important to protect the eyes, as it enables debris to be flushed out and the tears also contain chemicals to kill bacteria and destroy viral particles on the eye. Many animals produce a similar sound to a crying human to convey distress. Think of a puppy who's been left on it's own; the sound is so similar that it can easily cause a person to be just as distressed as when we here a baby human crying! Elephants, bears and some birds are other examples. I should add that, as far as I'm aware, we have no decent theories to explain why the use of tears to convey emotions was selected through natural selection. Our recent extant ancestral species, such as chimpanzees, rely on facial expressions and sound.