Any creature which has been trained specifically to fight alongside its handler, like an attack dog or equivalent.
Generally speaking, in order to qualify as an attack animal the creature must:
Not act (or at least it must not be supposed to act) without explicit instructions from its handler beyond a normal routine. This usually entails something with animal level intelligence which can be trained to obey. Sapient creatures can count if they still fit this criteria (that is they're forced to obey, choosing to because of Undying Loyalty or because they're being paid isn't an example).
They must be acting at the command of their handler (it's not enough for someone to throw their victim into a cage full of lions, they have to be able to make the lions attack them).
The "creature" does not technically need to be an animal (semi-intelligent drones or golems, artificial biological constructs or magical, elemental beings are all fair game).
Not be sent out to act on their own (like when summoning a bigger fish), since they're essentially a weapon, not a character (a good analogy would be that you send out soldiers armed with swords, not swords on their own).
This trope is likely derived from domestic animals which were used for their attack abilities (dogs being the most obvious). See the Real Life section for more details. Using a "weapon" like this often implies that a character is either nature loving and generally an all around good person who animals trust, a genius (possibly mad) who can create or control such things or evil, by virtue of "enslaving" them.
Super Trope to:
In One Piece, Doctor Vegapunk has apparently done extensive research into the nature and abilities of Devil Fruits, even making inanimate objects able to eat them. There have been a gun and a sword who have respectively eaten the Inu-Inu (Dog-Dog) Fruit: Model Dachshund and Zou-Zou (Elephant-Elephant) Devil Fruits respectively, resulting in a dog that sneezed explosive baseballs and an elephant that could transform into a sword. Of course, this being One Piece, it basically turns out just how you would expect.
Shirahoshi, the princess of Fishman Island, is the current incarnation of the Ancient Weapon Poseidon, which allows her to control Sea Kings.
Earlier and more straight examples included Mohji the Beast Tamer (who leaves all the fighting part to his giant lion pet) and Ohm the "Sky Breeder", who combines his deadly morphing sword with his extremely well trained giant dog Holy (so well trained, in fact, that he can even stand up and do kickboxing).
Basilisk's Hotarubi is a NinjaAction Girl who can send out insects to do her bidding and has a pet snake thar she can command as well.
Valerian features a number of creatures classified as "living weapons", most notably the iconic Scnarfeur, essentially an entire species of Bratty Half Pints with explosively caustic spit and instinctive hostility towards all living things due to originating on a Death World. They can be tamed by binding their head gland down, which turns them docile and allows them to develop a human-like personality, but they remain classified as animals and releasing the head gland will again revert them to their original state.
Word of God states that the Xenomorphs from the Alien franchise are these. They were created by the Engineers, or "Space Jockeys" as they're nicknamed, in preparation for their genocide on mankind, who they also had created, but their experiment with the Xenos and other stuff went wrong before they could use them.
The Heralds of Valdemar series has the Shin'a'in battlesteeds. Unlike your average warhorse, these have been bred over centuries to be the ultimate fighting mount (possibly with some magic help at the beginning). Smart, obedient, and capable of distinguishing and killing enemies without any direction, they make a deadlier team with a human than another human would. They're also good at tasks such as guarding camps and equipment, finding water in the forest, and carrying injured riders to get help. What they aren't good at is being pretty; looks had no priority in the breeding program and the steeds resemble roughly-carved horse-shaped granite.
Both Arthur C. Clarke and Stephen Baxter's works feature a plant designed to grow on the Moon, taking all its necessities from the lunar soil, and to germinate by firing its seed as a projectile. In Clarke's short story, the inventor unwittingly leans over the thing just as it germinates, with obvious results. In Baxter's novel Space, a similar creation is transplanted to Mercury, where it takes over the entire surface of the planet and plays the central role in Humanity's Crowning Moment of Awesome against the alien invaders.
The Leviathan series utilizes this as one of the main motivators of the plot itself. The entire Allied side (Darwinists) use genetically-engineered super animals as war machines. Not to mention the living airship...
In the web-novel Domina, the "fey" use bio-engineered monsters as weapons. They're too crazy to use them effectively, though, so they usually just throw a few out when they're bored.
Robert A. Heinlein's Tunnel in the Sky. When Johann Braun goes on his survival test, he takes along his pet, a big, lean, heavily muscled boxer dog named Thor with unfriendly eyes. Interestingly, they're both killed only minutes into the test.
Andre Norton's Beastmaster novels, such as The Beast Master and Lord of Thunder. Hosteen Storm was a Beastmaster who could telepathically command several animals. One of them was a sandcat named Surra who was highly effective in battle.
In the Sherlock Holmes novel The Hound Of The Baskervilles, a hound is specifically raised to look like the Hound of legend. It's used by its master to kill Sir Charles Baskerville via literally scaring the old man to death, and said master also intends to use it to kill Sir Charles's nephew and heir, Sir Henry.
In The Dark Tower, main character Roland must defeat his instructor in single combat and can only bring one weapon to the duel. His weapon turns out to be his hawk, David.
In The Horse and His Boy, Bree tells Shasta that as the war horse of the nobleman Ahoshta, he was trained as an attack animal and acted as such. While he does tell Shasta about his adventures, he always ended them by saying that he'd rather go back to Narnia soon and fight for the Narnian troops as an equal member of the army, not just as a warrior's steed.
In the Ciaphas Cain novel "Duty Calls", one of Amberley Vail's entourage is a former Commissar called Simeon who ended up in the penal legion and hooked up to a Combat Drug Injector (giving him multiple addictions). While he still acts like a normal(ish) human being, Vail can control him by controlling the drugs he's being given.
Subverted in Frasier. Martin has been staring at photos from an unsolved murder years ago. When he goes to take a break, Frasier glances at them and concludes a trained monkey was used to kill the victim. When Martin solves the case, Frasier assumes he was right about the monkey, but we learn it was a crooked cop.
In the Buffy the Vampire Slayer episode "The Prom", Andrew has hellhounds, which his brother Tucker bred and trained to attack the people at said dance. Not to mention, as Andrew will remind you, he trained flying demon monkeys to attack the school play.
Highlander had an episode with an immortal named Kanis, who used his pack of dogs to bring down his quarry. Duncan managed to throw a wrench in things when Kanis tried it on him, using a female dog in heat.
In an episode of Bones a dog is used by its owner to kill a vet looking into dog fighting. Booth & Brennan are quite clear that a person killed him using the dog as a weapon.
Alex's landlord, Jim, in the Doctor Who episode "Night Terrors" has a mean dog which he uses to threaten Alex.
Eaglebones Falconhawk from The Aquabats! Super Show! can summon an invisible female bird called The Dude. So far, The Dude has only helped Eaglebones without clear instruction twice (once in "EagleClaw!" to take away his brother EagleClaw's guitar and once in "Showtime!" to take SuperMagic PowerMan's headband after Jimmy the Robot removes it from Space Monster M's head) but in her other appearances she follows this trope.
In one episode of Columbo, a man uses his trained Doberman Pinschers to kill at the command word "Rosebud". Columbo turns this on its head by having the dogs retrained, so that when the culprit tries to get rid of Columbo the same way, all he gets is a savage face-licking.
Very early in the life of Garfield, Jon tried to train the eponymous feline into an attack cat, but only succeeded in getting himself mauled.
Warhammer 40,000's Tyranids are an entire species created to serve as weaponry, controlled by other species, which are seen as the same family as the weapons.
Also from Warhammer 40,000 are the Orks. They are believed to be created by a group of beings called Brain Boyz as a weapon against the Necrons. They are quite effective weapons against them, unfortunately the same is true of everyone else. Of course technically the Brain Boyz were themselves created to be their controllers by the Old Ones.
Squigs are small, aggressive critters that Orks frequently keep as pets and train to attack people on command. The largest of all squigs is the massive Sqiggoth, which grows to be as big as a Baneblade tank.
The Chaos Demons have beastly feral demons that are more animalistic. Khorne has Flesh Hounds a cross between a dog and a lizard, Nurgle has Beasts of Nurgle butt ugly wretches that have dog like intellect, Tzeentch has Screamers flying manta rays with tusks, and Slaanesh has Fiends of Slaanesh which are centaur like creatures with lobster like claws and scorpion tails.
Forgotten Realms prehistory says wyverns were created as weapons by Aearee (ancient bird-like creatures). Local Precursors are called "Creator Races" for a reason.
Wizards constantly try to customize some or other Hybrid Monster or The Undead for that purpose, though it rarely ends well. Akhlaur has "cat-man warrior" project, for example.
Early editions allowed Player Characters to buy war dogs that would fight alongside the party. Since they were almost as effective in combat as a 1st-level character, they could greatly increase a party's chance of survival at low levels.
Druids and rangers have the "animal companion" feature, granting a creature who loyally serves the character during adventures. It's more an extension of the character as opposed to its own entity, automatically scaling in strength as its master gains experience.
Sourcebooks also allow characters to construct various types of golems.
Stormbringer Companion supplement, "Sea Battle at Melnibone" solo adventure. One of the opponents Elric faces during the battle is a sea captain who has a war hound of Chalal fighting at his side.
Mongoose Publishing's Starship Troopers - The Roleplaying Game. Neodogs have cybernetically enhanced teeth and jaws, allowing them to enter combat alongside their handlers. In the original Robert A. HeinleinStarship Troopers novel, neodogs did not have such augmentations and were used for intelligence gathering, not fighting.
BIONICLE: The Order of Mata Nui used trained Energy Hounds, most notably one in Mahri Nui named Spinax. Also in Mahri Nui, Toa Jaller had a Hahnah crab that, at least in his toy set, was equipped with a gatling cannon for him.
Fina from Skies of Arcadia uses her pet (a creature called Cupil) as a weapon in precisely this manner.
The majority of monsters in the Resident Evil were created to be these. Although the ones that could follow orders had an alarming tendency to become...less controlled.
Similarly The Virus in Prototype, but this is more of a subversion, as the scientists of Blackwatch tried this and had it turn on them twice. The slavering zombies and various hideous flesh-beasts created when the virus finds human carriers do serve quite well as weapons, whether you prefer quantity or style, but exactly four, all non-human beings in the world are capable of controlling its spread and the creatures created, and there's nothing on Earth that's going to control them.
In Cave Story, a mimiga who eats one of the red flowers would grow exponentially larger, stronger, and more resilient. They then lose their minds and normally go uncontrollably berserk, but a person who wears the Demon Crown is capable of controlling them and making them fight at his side.
In BlazBlue, the Kaka clan (and by extension Taokaka, one of the playable characters). They were created from Jubei's DNA to combat the Black Beast almost 100 years earlier, can only reproduce (asexually) if there are less than 100 of them and can process Seifer naturally and use it to manifest glowing energy claws.
Rachel Alucard has a frog called George XIII hop towards her opponent and electrocute them as a ranged attack.
When Hazama created Mu-12 by brainwashing and forcefully transforming (or upgradingher without the "safeties" on if you look at it that way) Noel Vermillion, he more or less wanted her for this. Even referring to her as his "sword".
Lambda-11 is treated this way by Kokenoe (although she feels bad about turning her into an Empty Shell for this purpose). Tager might also count, but he's sufficiently loyal the issue of whether Kokenoe can force him to obey hasn't come up.
The eponymous creatures from Metroid are more or less weaponized space-jellyfish. The problem is that no one seems to be able to control them too well. The only being capable of it was Mother Brain, and even then it wasn't complete. Indeed, a Metroid ends up being one of the primary factors in her death. This didn't stop the Space Pirates from trying, of course.
As mentioned above the Zerg race from Starcraft are pretty much the same story as the Tyranids of Warhammer.
Hunter Pets in World of Warcraft. Warlocks and Deathknights have pets too, but they are either demonic or undead.
The Zuul in Sword of the Stars were originally created as weapons by the Suul'ka against a Morrigi colony. They were especially designed to be ravenous and fast-multiplying in order to quickly kill and consume all living things on the planet and die off. Unfortunately, the Zuul prove themselves masters at Mind Rape, allowing them to quickly learn the secrets of the target population, build spaceships, and escape into the universe. They are also extremely devious (at least, the males are; the females are mindless brutes; all by design).
In Ace Attorney Investigations 2, the blind assassin Ryoken Houinbo trained his guide dog to kill, to the point where it's considered one of his trademark weapons.
In Minecraft, once you tame a wolf by feeding it, it will follow you unless you command it to sit, and it will attack mobs that attack you.
Dragon Age has Mabari War Dogs; Highly trained and highly loyal attack dogs in use by the nobles and army of Ferelden. They are also possessed of at least some measure of intelligence; when Ferelden was formed by rebelling against The Empire the Mabari defected to the Ferelden side en mass, and they are often remarked to be "smart enough not to talk" (a few characters seem to understand Mabari as well).
Several enemies in both games can also drop turrets.
Gaige the Mechromancer has her "D374-TP", DT, which works similarly to a cross between the turrets and Bloodwing (mainly using melee attacks like Bloodwing, but staying out and attacking for a limited time rather than just striking an enemy once).
Mass Effect brings us the varren, which are not only vicious, deadly creatures without outside influence, but which are also trained and used as attack animals by groups such as the krogan, as well as batarian mercenaries.
Dogmeat and Rex in the Fallout series. In Fallout 3, one of the Scavengers has an attack Yao Guai, and the Enclave uses Deathclaws in this manner.
Call of Duty: Ghosts has a German Shepard named Riley who can be controlled and attack enemies stealthily.
Besides dogs, many warhorses were like this, trained to bite, kick, or stomp at their rider's command.
In Britain, there is a stereotype associated with "chavs" of them owning vicious dogs which they use to threaten people with.
It's actually a pretty common steteotype in regards to gangsters of almost all countries. For the time being, their preferred "breeds" tend to be Pitbulls.
The Roman Army had large units of war dogs. However, unlike almost any other types of military units and weapon technology, there are no known reports that describe their tactical use in great detail. Either they were mostly for show, or the Romans didn't want their enemies to know about them.