Never breed any animal that has temperament problems. In particular, this has been the cause of the degeneration of many breed's general temperament: Doberman Pinschers, Rottweilers, and so on. If your animal is untrustworthy around people, overly aggressive to people, excitable, or is a fear-biter, do not breed it. If it is shy or submissive, don't breed it. Look for happy, confident and obedient animals, and consider carefully the particular temperament requirements for your dog's breed.

There are a variety of tests to indicate a dog's temperament. Many of the working breeds have a temperament test (for example, the Doberman's WAC test) for their breed. See if there is a Canine Good Citizen test (open to all dogs) that gives some indication of the dog's temperament (and, yes, training). Therapy Dogs International and other Therapy Dog clubs have temperament testing that does try to separate out actual temperament from training. Obedience titles can be (but are not necessarily) an indication of good temperament.