For anyone who has seen their dog sleep, the answer is clearly yes. But the scientific answer is, "we do not know." We know that the dog experiences REM, or rapid eye movement sleep. REM sleep associated with dreams, but we know that people at least, rapid eye movement during sleep is not necessarily indicative of the dream. Our best guess is that dogs do dream, but no way to prove it, because we can not ask them.
How do we distinguish REM sleep in a dog?
Look in the eyes of a sleeping dog, and you will notice that periodically, eyes moving back and forth in a fast rhythmic motion. It is recognized as Rapid Eye Movement, or REM, sleep. Many dogs will also move their lips and beard and make a licking and chewing movements when they sleep. They can paddle their feet, almost as if they were running. Some dogs will vocalize, do a little yips and howls.
Are owners sometimes concerned about this problem?
Some people have seen this behavior when their dog is sleeping, and this fear is a kind of a seizure. So how do you know about what your dog is doing is normal?
If a dog is sleeping normally, he easily awakened by calling his name or pushed into her body. If a dog has a seizure, you would not be able to stop a dog from seizure using the same technique.
But a word of caution: Be careful when a dog waking from a deep sleep. When disturbed from a sound sleep, many dogs instinctively try to bite before they even awake.