When you mix two or more separate gene pools, the recessive genes that carry the health problems are buried. As a result, you get a healthier animal. Simply put, mixed-breed dogs are, in general, healthier than their purebred cousins and typically require fewer visits to the veterinarian. Mixed breeds are also more temperamentally sound than purebreds. Not all chows are aggressive, not all cockers have a nervous tendency to bite and not all retrievers are gentle, but generalizations about breed temperament often hold true, at least to some extent.
Mixed breeds are typically less extreme temperamentally.
Character and behavioral traits do manifest in mixed-breed dogs, but in a diluted form. There is a final, compelling reason to adopt a mutt rather than a purebred. Our shelters are filled with primarily mixed-breed dogs in need of good homes. With the tragedy of pet overpopulation still far from being solved, I can't see perpetuating a market for yet more dogs. They're cheap, reliable and what nature intended in the first place.