There’s a Boston terrier snoring under my desk as I write this, and his presence may be making me more productive.

A 2012 Virginia Commonwealth University study found people who bring their dogs to work report less job stress and greater job satisfaction. And it isn’t just the dog’s owner who benefits. For many people, petting a dog — any dog — can reduce stress, and having one present in the office can increase overall employee health and morale. The VCU researchers...