There may be another unexpected benefit to having a pet dog in childhood - a lower risk of developing schizophrenia later in adulthood. A recent study (conducted in the Baltimore, MD area) found the lowest risk of developing schizophrenia was in individuals who were exposed to a pet dog from birth or before the age of 3. So... early childhood exposure to household pet dogs is best.
On the other hand, there was no significant link between pet dogs and bipolar disorder, or between pet cats and either psychiatric disorder (schizophrenia and bipolar disorder).
Interestingly, the lower risk of schizophrenia in those having a household pet dog before the age of 3 matches research finding a lower incidence of allergies and asthma in those with early childhood exposure to pet dogs (and also pet cats). There could be a number of reasons, but one popular one is that the exposure to the dog microbes in early childhood influences the child's gut microbes and affects the immune system in a beneficial way.