"In sum, if we define crying as tearful sobbing, then we know that humans are the only primates that cry. If we define crying as emitting vocalizations that co-occur with distressing situations, then we can conclude that most monkeys and apes cry, especially as infants. If we are really asking whether humans are the only primates that feel sorrow, then we do not know the answer. Yet."
http://www.scientificamerican.com/article/are-humans-the-only-prima/