Affection without any ambivalence," rhapsodized Sigmund Freud, "a feeling of close relationship, of undeniably belonging together." He was speaking not of mothers or even of psychoanalysts but about Jo-fi, his pet dog. Americans understand. An estimated 52 million dogs reside in U.S. homes. Also 56 million cats, 45 million birds, 250 million fish and 125 million other assorted creatures. Yet despite the antiquity and ubiquity of the human-animal bond, neither Freud nor anyone else has shed much scientific light on the phenomenon. "Animals are so taken for granted," says Alan Beck, director of the University of Pennsylvania's Center for the Interaction...