I was listening to a very interesting interview with Anderson Cooper from CNN called "The Smartest Dog in the World". The brains of dogs were analyzed in different situations. An interesting conclusion is that when dogs and humans make eye contact, oxytocin is released from both the dog and the human. Oxytocin triggers feelings of love and protection. Like when a parent looks into a child's eyes.
Dr. Brian Hare, with Dognition believes that when a dog is looking into your eyes, "he is hugging you." Hmmm, assuming he is not trying to bite you. That's nice, now what about a cat?