Although a dog is able to breathe through his mouth, he typically breathes through his nose. The most common occurrence of mouth breathing in a dog is when he is panting.
Certain illnesses sometimes prevent a dog from breathing through his nose because of blocked nasal passages. The owner is not always aware of this condition unless the dog becomes excited or very active. Dogs fall ill to certain respiratory infections that affect their breathing, and foreign bodies sometimes get lodged in the nasal passages producing inflammation and trouble with breathing. Panting when a dog is hot or thirsty is not a cause of concern, but if he is panting unusually often or is breathing with his mouth open, a trip to the vet is warranted.