Magical Girl Lyrical Nanoha: Fate and Arf in the first season. Not so much in later seasons, which has Arf both spending less time in her wolf form and spending less time together with Fate.
Neo Human Casshern: Casshern travels with his dog partner Friender. Friender was originally the family dog — brave and fierce, who got killed, but was revived as a trusted companion. Friender can become a tank, car, jet, or a submarine, and can breathe fire. He is the inspiration of Rush.
The Sandman: Delirium has Barnabas, who she picked up from her brother Destruction.
Delirium: I can't look after a doggie.
Barnabas: You misheard him. I get to look after you.
Groo The Wanderer: Groo has Rufferto. Writer Mark Evanier once pointed out that Groo couldn't have a human sidekick unless that sidekick was stupider than Groo, but a dog that would always see him as smart and heroic would be ideal.
I Am Legend The protagonist has a pet dog. Since a viral outbreak nearly eradicated humanity, this dog is the protagonist's only company, and pretty much the only thing keeping the crushing desolation from driving him insane.
The chaps of Three Menina Boat have the canine delinquent Montmorency.
I Am Legend: The Dog in the original short story is a subversion. The survivor tries to tame a feral dog into his companion. he appears to succeed in getting the dog to take food from him, and then you find out the dog died two weeks later due to illnesses.
The Dresden Files: Harry's dog Mouse goes all sorts of places dogs don't usually go.
Haplo, Anti-Hero of the Death Gate Cycle, has a dog that goes everywhere with him, even when this defies all logic or common sense. It turns out that the dog, unknown to everyone, is actually a magical manifestation of Haplo's soul.
In The Silmarillion story of Beren and Luthien, the title characters are accompanied on their adventures by the wolfhound Huan.
Oleg Divov's The Dog Master features an entire paramilitary organization where specially-equipped soldiers hunt zombie-like creatures with their dogs. They are led by the titular Dog Master. Neither the dogs nor their masters survive the final battle with the zombies.
In John C. Wright's The Golden Transcedence, Phaethon populates the bridge with mannequins of famous explorers. Including the dog of one such explorer, because it was just not right to have that man without his dog.
Fallout: Dogmeat, a dog which the player can have join their party, makes a cameo (and acted as a non-canon bonus character) in 2 and appears (in 3D for the first time) in 3 . He's found next to a dead body named Max, a homage to Mad Max 2 and his dog, Dog. Fallout: New Vegas also gives you Rex, a partially cybernetic dog companion.
Many players have been known to Save Scum should their dog companions die in Fallout. Human companions, meanwhile, are generally considered expendable.
In Fable II, the protagonist gets a dog to help fight off enemies and find buried treasure. You get a dog on Fable III as well.
Tales Of Vesperia has Repede, a damned big dog loyal to Yuri, the main protagonist. Oh, and he's a playable party member as well.
The Shinobi sequel Shadow Dancer had Yamato, who you could sick on enemies to prevent them from attacking.
In Dragon Age, you have an opportunity to get a Mabari hound into your party, unless you're a Human Noble, then you've had one for years. Ferelden loves dogs.
In Dragon Age II, the Black Emporium DLC provides a Suspiciously Similar Substitute for the original Mabari. This time, the dog is treated much like a ranger's summoned animals were in the original, so he no longer takes up a party member slot and can be with you at all times.
Deadly Premonition has Forrest Kaysen's dalmatian Willie, who is exceptionally good at tracking down missing people. According to Word Of God, it also relays orders to Kaysen from the Red World.
The Dead to Rights games has Shadow, an insanely vicious husky capable of killing Mooks as well as his Cowboy Cop partner Jack Slate as well as being able to solve puzzles or get various objects needed for Jack to progress.
Minecraft recently introduced wolves, the first mob that can be tamed. They'll follow you around and help you fight, whether that means defending you from hostile mobs or hunting down passive mobs that you have targeted.
Missile from Ghost Trick. Possibly the greatest example ever.
Dog from Half-Life2, although his (it's?) body moves more like a gorilla, but the way he acts and his function in the game are both clearly dog-like.
Dog/Worthless Mutt from Arcanum. He can join your party without taking up a companion slot and train himself to be a melee master.
Web Original
Played straight with Wolfie in Far Lands Or Bust, but subverted in Mindcrack Ultra Hardcore, where Kurt's wolves have been responsible for his deaths in both seasons 5 and 6.
Various celebrities, mostly females, at one point or another carried a small Chihuahua or similar with them in their handbag as a fashion accessory. The self-proclaimed "Fashion Czar" Rudolf Mooshammer from Munich, Germany also had one called Daisy that he carried everywhere he went.