The following is a list of unnamed individual pets.
Canines[]
Amanda Rogers' dogs []
These three dogs were owned by Amanda Rogers. Her foster parents referred to them as "The Zoo". (TNG: "True Q")
Cerritos crew member's dog []

An officer's dog aboard the Cerritos
This female dog belonged to an officer on the USS Cerritos.
In 2380, Ensign D'Vana Tendi encountered this dog in the ship's lounge while it was being walked by its owner. While the owner spoke with another officer, Tendi approached the dog, shook its paw, and introduced herself to it, only to become disgusted after it licked her face. (LD: "Much Ado About Boimler")
Harewood dog[]
A dog sat in bed next to Rima Harewood in 2258 of the alternate reality.
A photograph of the same dog adorned Lucille Harewood's hospital room at the Royal Children's Hospital. (Star Trek Into Darkness)
Hysperian royal's canine []

The Hysperian royal's dog
A female member of Hysperian royalty had her portrait painted with her Alfa 177 canine. (LD: "Where Pleasant Fountains Lie")
Janeway's scapegoat dog []
As a child, Kathryn Janeway spilled her sister Phoebe Janeway's paints accidentally, blaming it on their dog. (PRO: "Mindwalk")
Lost puppy []
This puppy went missing while on the USS Enterprise-D. Sito Jaxa located it while filling in as operations officer for half an hour. (TNG: "Lower Decks")
Mollie's litter []
Sometime prior to 2374, this litter of puppies was born to Kathryn Janeway's dog, Mollie. Mark Johnson found good homes for them, which he related in a letter to Janeway. (VOY: "Hunters")
Paris' dog(s) []
These dogs belonged to Tom Paris. In 2371, upon being asked by Captain Janeway whether he liked dogs, he replied that he did, and had always had a dog. (VOY: "The Cloud")
Porthos' mother []
This beagle was a female dog belonging to Jonathan Archer's ex-girlfriend's mother. Archer recalled being crazy about the dog, which prompted her owner to call him when the dog became pregnant. Her litter consisted of at least four males: Athos, Aramis, Porthos, and D'Artagnan. (ENT: "A Night in Sickbay")
Troi family dog []

The Trois' pet dog
In 2336, this dog accompanied Lwaxana Troi and her family on a picnic. Kestra Troi chased after the dog, which led to the former's subsequent death by drowning. (TNG: "Dark Page")
Equines[]
Hysperian horses[]
In 2381, at least four horses were present in a stable area aboard the Hysperian ship Monaveen. (LD: "Where Pleasant Fountains Lie")
Pike's horse[]

Pike's horse
Christopher Pike was riding this horse when Robert April's shuttle landed, spooking the creature. (SNW: "Strange New Worlds")
|
Felines[]
Data's anti-time cats []

Data's cats
In an anti-time future, Data kept several cats as pets. (TNG: "All Good Things...")
Ensign's cat[]
Data wept when he saw an ensign feeding his cats. (PIC: "The Last Generation")
Mark Johnson's kitten []
This kitten belonged to Mark Johnson. In a letter he wrote to Kathryn Janeway in 2374, he mentioned that Mollie's puppies got along well with it. (VOY: "Hunters")
Agnes Jurati's grade school cat[]
Agnes Jurati had a cat in grade school that she still missed sometimes. (PIC: "Assimilation")
Ariana La Forge's cat []
This cat belonged to Ariana La Forge. She trained it to jump into her arms on command by walking around for two months with a piece of tuna in her blouse. Geordi La Forge related the story to Data in 2370, when he was looking for advice on training his cat, Spot. (TNG: "Force of Nature")
Spot's kittens []

Spot's litter
These kittens were born to Spot in 2370. Unlike their mother, they did not have the intron virus. Study of these kittens was instrumental in finding a cure. (TNG: "Genesis")
Deanna Troi's Betazoid kitten []
This Betazoid kitten belonged to Deanna Troi. It did not get along with Troi's mother, Lwaxana. (TNG: "Pen Pals")
Twelve male felines []
These twelve male cats lived aboard the Enterprise-D as of 2370. Data noted this when discussing Spot's pregnancy with Reginald Barclay, saying any of them had an equally likely chance of being the father of these kittens, as Spot had escaped from his quarters many times. He intended to run a full DNA analysis to determine which one fathered the litter. (TNG: "Genesis")
Tasha Yar's cat[]

Yar's cat
One of the few bright spots in Tasha Yar's life was finding a cat, which she attempted to protect while being chased by a rape gang on Turkana IV. (TNG: "Where No One Has Gone Before")
Others[]
Billups' dragons []
Andarithio Billups had pet dragons at his castle on Hysperia, as he told his mother, Queen Paolana, that "[he didn't] want to live in a castle with pet dragons and all the mutton [he could] eat." (LD: "Where Pleasant Fountains Lie") In 2382, Paolana sent another such dragon to the Cerritos, which ended up heavily charring Billups. (LD: "Shades of Green")
Kruge's monster dog []

Kruge's monster dog
Commander Kruge kept a ferocious monster dog as a pet aboard his Bird-of-Prey, to the left of his command chair. Kruge ordered one of his crew to feed the animal, a task another crew member regarded with fear. It died when, during the Battle of Genesis, two photon torpedoes from the USS Enterprise hit the ship, seemingly causing a power overload and possibly electrocuting the animal. Distraught by the animal's death, Kruge briefly held its corpse in his hands. (Star Trek III: The Search for Spock)
Jil Orra's wompat []

Jil Orra's wompat
This wompat was kept as a pet by Jil Orra. In 2369, before beginning to interrogate Jean-Luc Picard again, her father cautioned her to take good care of it, as it had been recently separated from its mother. (TNG: "Chain Of Command, Part II")
Sabor's blazzard []

Sabor's blazzard
This blazzard was kept as a pet by the Orion Pirate Queen Sabor in 2382. It was present in the Guildhall on Orion, where it sat on a perch by her throne. (LD: "Shades of Green")
Subspace mesomorph []
This creature was the pet of a Lyridian child. In 2375, the Think Tank invented a new type of scanning technology to locate it after it went missing. (VOY: "Think Tank")
Teneebian skunk []
This Teneebian skunk was kept as a pet by a child living on the ECS Fortunate in 2151. (ENT: "Fortunate Son")
T'Pol's sehlat []
A domesticated sehlat belonged to a young T'Pol. While traversing Vulcan's Forge in 2154, she recalled this to Jonathan Archer after they had just been chased by a wild sehlat. (ENT: "The Forge")
Targs[]
Bargh's targ []
Bargh, head of the Klingon Oversight Council, kept a massive targ as a pet. In 2382, Bargh incorporated his giant targ into the second trial of the Ritual of J'ethurgh, and had Ma'ah and his three companions attempt to incapacitate it. When Ma'ah's brother Malor, aided by Lieutenants jg Beckett Mariner and Brad Boimler, tied the beast's legs together, Bargh then demanded that Ma'ah and his companions trim the targ's nails and express its anal glands, but Mariner stated that the targ was simply his pet, and told Bargh to "hire a targ groomer". After Ma'ah slayed Bargh in battle, Ma'ah and Malor ended up adopting the targ, who stayed on their family farm alongside Dorg's targ. (LD: "A Farewell To Farms")
Dorg's targ []

Dorg's pet targ
Bargh's brother Captain Dorg had a pet targ that he kept aboard his vessel, the IKS Che'Ta'. When Ma'ah challenged Dorg for command of the Che'ta' in 2381, this targ interfered and attacked its owner, prompting Dorg to assault his own pet. After Dorg was slain by Ma'ah, the targ seemed to gravitate towards the victor, who seemingly reciprocated the pet's affection. (LD: "wej Duj") The targ was on the bridge later that year when the Che'Ta' was attacked and captured by the Nova One. (LD: "Twovix") By 2382, the targ was living on Ma'ah's family farm, where it was later joined by Bargh's targ. (LD: "A Farewell To Farms") After Ma'ah was given command of Relga's fleet, the targ was on the bridge with him of Ma'ah's new flagship. (LD: "The New Next Generation")
Martok's targ []
Martok had a pet targ from boyhood, which he described as "a filthy, mangy beast", but with "the heart of a warrior" nonetheless. His new wife Sirella hated the creature, so much so that upon moving into Martok's home, she left the door open for the animal to escape. Martok never saw it again. (DS9: "Strange Bedfellows")
Relga's targ []
Like her brothers Dorg and Bargh, Relga had a targ. Though small, her targ appeared to be far more vicious than her brothers'. When Relga's Bird-of-Prey was hit by the Schrödinger possibility field, her targ devolved into an oyster, and was ultimately killed by the subsequent destruction of the ship. (LD: "The New Next Generation")
Worf's targ []

Worf's pet targ
This targ was the childhood pet of Worf. Decades later, when the Enterprise-D found itself at the edge of the known universe in 2364, this targ briefly appeared to Worf and Tasha Yar on the bridge. (TNG: "Where No One Has Gone Before")