Dogs produce real tears. The tears are to keep their eyes wet or to rid them of debris. Some dogs have over-active tear ducts, and this condition can cause tearstains around their eyes.
Dogs are able to experience anxiety and depression. Some dogs have anxiety disorders in which they portray symptoms like fear, whining and other behaviors. Some dogs may go through a stint of depression in which their activity level decreases, they sleep more and they want less attention from their owner or other animals. However, dogs do not cry like human beings. The way that a dog cries is by making a high-pitched sound, which is called whining.