The domesticated dog (Canis lupus familiaris) was the most common canine species found on the planet Earth. A juvenile dog was known as a puppy. Dogs were capable of being trained to do certain tasks, such as "fetching", and were also capable of forming very close bonds to their master, almost symbiotic in nature.
When living on Earth, Amanda Rogers owned three dogs, which her parents referred to as "The Zoo." After seeing the size of her quarters aboard the USS Enterprise-D, she told Commander Riker that she had enough room for her zoo. She then told him she would have a dozen dogs if she could, but her mother said, "Enough is enough." Amanda accidentally created a litter of puppies in her quarters, using the powers of the Q, but was able to make them disappear. Later, Q transformed Doctor Beverly Crusher into a dog, apparently without her knowledge, in order to prevent her from interfering with Amanda. Amanda was able to restore her to Human form. (TNG: "True Q")
The Trois owned a little dog when Deanna Troi was still a baby. Her sister, Kestra Troi, ran after the dog when it got away. Because she was out of their sight, the Trois noticed too late that Kestra had fallen into a nearby lake and drowned. (TNG: "Dark Page")
When Porthos was sickened due to a pathogen on the Kreetassan homeworld, Captain Archer had a dream about Porthos' burial. It was at a "dog cemetery" with several tombstones, including ones for Duffy and Goldie. These may have been previous dogs of his. (ENT: "A Night in Sickbay")
Ensign Sito Jaxa told Lieutenant Worf, in Ten Forward in 2370, that among her duties at ops was to use the internal sensors to find a lost puppy. Worf told Sito that the ops duties are a different challenge than the tactical duties. (TNG: "Lower Decks")
When he accidentally traveled back in time with Quark, Rom and Nog to 1947, Constable Odo disguised himself by turning into a German Shepherd dog, popular among Earth military at the time. (DS9: "Little Green Men")
The Baneans domesticated a creature very much like dogs, whether or not they were native to their homeworld. Tolen and Lidell Ren's dog, Neeka, was instrumental in proving the innocence of Tom Paris. (VOY: "Ex Post Facto")
Breeds of Earth dogs