I can't take the stance that breed or pedigree are insignificant, especially with dogs.

People should do a lot of research into the type of breed of dog they are getting. Terriers and Great Danes are completely different balls of wax, with different temperamental and physical issues to be aware of.

So while mutts are often wonderful, they can carry traits from their pure-bred parents. With this in mind, I can understand if someone wants a pure-bred dog in order to avoid the complications of certain breeds (you might not want a herding dog in an apartment, or a sledding dog in southern florida, or a dog that will aggravate your allergies, or a dog that will get very large if you have small children). So many dogs are sent to shelters because people didn't do their homework on the breed they were bringing home.

Second: pedigree is important in pure-bred dogs. Good breeders avoid breeding dogs with medical problems and bad temperaments. The things that make for good show dogs also make for good and healthy pets. People who don't know what they're doing shouldn't be breeding dogs. (Side story: my sister bought a shitzu puppy for her son from a friend of a friend who just happened to have two dogs she let have sex. Out of a litter of 5, 2 died at birth, and the little bundle of fuzz she brought home suddenly started coughing up blood at 4 months old, and later died of a heart defect. My sister and nephew were heart broken.) Good breeders have their puppies checked for medical issues before they are sent to their forever-homes, and require that their dogs be returned to them if the dog becomes unwanted; not to a shelter.

So yes; adopt when you can, if you can. But definitely do research on the breed you are bringing home. And always have your pets fixed!