I currently own three dogs, and not a single one of them is a pedigree. Loki is a dog that I "inherited" from my cousin and appears to be a German shepherd mix. Gracie may be part lab and may also be part Chow; we're not really sure. And Daisy, Who we saved from the shelter appears to be a Lab mix. I love all three of my dogs equally. They are all in excellent health , and have great dispositions, though the younger ones can still get into trouble from time to time. My dogs are "mutts", and I wouldn't have it any other way.
Purebred dogs can be very expensive, and can be an expensive mistake if the dog breed is not suited for your families needs. Neither the Dalmatian, Chihuahua, or Jack Russells, which have enjoyed temporary popularity, are a good choice for families with young children. Many of these breeds have been adopted and sadly later returned for these very reasons. They were not the right fit for the family. Many purebred dogs can also be more prone to certain genetic health traits such as hip dysplasia, simply because they become "inbred", and can more easily pass those genetic traits on.
Mutts, on the other hand, are mixed breeds, which helps in decreasing their chances of passing on poor genetic health traits. The mutts that I have had, all have had good dispositions, and most were fairly smart. I have yet to see any purebred puppies who were cuter than my mutts are.
Sadly, many mutts, or mongrels, are unwanted. Many of them will be left or abandoned as strays, or taken to animal shelters, where the majority of them will be euthanized. The biggest factor in my adopting mutts is the satisfaction of knowing that I saved a dog from being "put down". I am fortunate enough to enjoy the companionship of my "mutts" and give them the loving home they deserve.