A heartwarming story told through the ages: Something unique enters a young man's (or woman's) life, and they form a bond that changes them forever, usually starting them down the path to adulthood.
What that something is, however, varies widely. From the classic "A Boy and His Dog", all the way to... well, keep reading, you'll see.
Be warned, however, that whatever X is can easily fall victim to Death by Newbery Medal, especially if it's of the huge and/or monstrous variety.
See also Interspecies Friendship. Compare Interspecies Romance and Magical Girlfriend, if relation with X is romantic and Attack Animal for less innocent partnerships.
Admittedly, the Shinigami is promising all along to kill the boy one day, while the boy quite calmly uses the Shinigami's apple addiction to get things from him (and the Shinigami ends up fulfilling his promise to murder the boy), but still.
Also played straight with a Girl and Her Shinigami where the Shinigami not only loves the girl but is willing to die for her.
The origin story of Maggot (a South-African mutant whose digestive system was two semi-autonomous slugs that could eat anything) was titled "A Boykie and His Dinges." Translated from the South-African slang the flashback was written in, that's "A Boy and His Things."
Kitty Pryde and Lockheed, a Girl and her Dragon. Subverted with the discovery that Lockheed is a sentient and intelligent creature, forced to spy on the X-Men for SWORD.
Marvel Comics' Earth X series had Bruce Banner in the body of a child and the Hulk separated from him into a creature that follows him around. A Supergenius Boy and His Rampaging Green Monster.
Alex Ross has said the visual was based on the obscure Marvel characters Moon Boy And Devil Dinosaur, who were A Homo habilis Boy and His Tyrannosaurus. (Yes...)
The comic book series Top Dog had a dog who was also a spy. Around almost everyone else, however, he had to pretend to be a regular dog.
In a scene from The Badger, Norbert pets Lamont, his North American "Buffalo." The villain promptly comments, "Ain't that sweet? A Deranged Individual and His Bison." (Hey, at least he was biologically accurate.)
The Bartimaeus Trilogy has one in Ptolemy and Bartimaeus, they'd have died for each other...one did . Then there's Nathaniel and Bartimaeus that comes after Ptolemy dies (way after, 2000 years plus), though they may not be an example as they both loath each other until the end and continuously argue (hilariously) throughout the whole three books.
The Temeraire series: A Boy and His Dragon. Or, possibly, A Dragon and His British Naval Officer. While not guiding Laurence into manhood, Temeraire does mark a significant shift both in his life and understanding of the world. The series also has several other variants on the trope, such as An Action Girl and Her Dragon, An Action Mom and Her Dragon, A Dragon and Her Conqueror of Continental Europe, A Dragon and His Overweight Middle-AgedCaptain; etc.
Dogsbody by Diana Wynne Jones is almost a standard A Girl and Her Dog story. Except that it's told from the perspective of the dog, who is actually a reincarnation of the guardian spirit of the star Sirius.
Both Jacob Two-Two and the Dinosaur (Mordecai Richler) and Henry Hollins the Dinosaur were A Boy and His Dinosaur stories.
The Harlan Ellison story A Boy and His Dog twists this trope: The boy is a serial rapist and the dog helps him find victims. The boy really does seem to love him, and finds his dog . . . food.
The book A Kestrel for a Knave (adapted for film as Kes) follows A Boy and His... well, you can guess, can't you? It also falls prey (no pun intended) to Death by Newbery Medal.
The City and the Stars: A Boy and His Noncorporeal Psychic Superintelligence from Before Civilization Fell. But really, Hilvar is an adult with a penchant for strange pets. Nonetheless, his people are psychics, and that allowed him to make contact with Vanamonde.
C. S. Lewis's Narnia, one of the books is titled The Horse and His Boy, which sometimes plays the trope straight and sometimes inverts it, as the boy is not always in charge, and is less experienced in the ways of the world than the former warhorse.
Another Discworld novel, The Truth, gives us Gaspode and Foul Ole Ron, who are essentially A Dog and His Insane Hobo.
Very similarly to The Horse and His Boy, in Fredric R. Stewart's Cerberon, the eponymous unicorn has been George's best friend his entire life. The novel opens with George clearly in command, but by the end it's Cerberon who is in charge. In a Shout-Out to C. S. Lewis, Cerberon's mother is named Jewel, after the unicorn in The Last Battle.
In one of Robert Rankin's Brentford stories Omally (always spelled without the apostrophe, for some reason) refuses to die without his faithful Marchant. Pooley comments, "A boy and his bike! I feel sick!"
In her Dragon Jousters quartet, the only way to have a truly tame dragon (instead of one you merely keep placid with drugs) is to hatch it and raise it from the egg. Love ensues.
In her Elemental Masters series, specifically The Wizard of London and Home from the Sea, characters Nan and Sarah have familiars, Neville the raven and Grey the parrot, respectively.
Flinx and Pip, of Alan Dean Foster's Humanx Commonwealth series, is a straight example. Flinx is The Empath, and Pip is an Alaspinian miniature dragon, or minidrag, that forms a psychic bond with him as a child. She amplifies his empathic powers and does a pretty fair job of protecting him.
Tamora Pierce loves this trope. There are two instances of A Girl and Her Cat (incidentally the same cat), followed by A Girl and her Every Animal In Existence, Including Skeletal Dinosaurs and a Baby Dragon, But Especially the Badger God, A Man and His Skeletal Dinosaur, A Girl And Her Horse, Sparrows, Griffin, and Small Children, A Girl And Her Crows, and A Girl and her Pigeons. And that's just in the Tortall Universe. The Circle of Magic adds A Boy And His Plants and A Girl And Her Starling to the list.
Walter Farley's The Black Stallion series is very much A Boy And His Horse. So was his Island Stallion series.
On Dog With A Blog, Stan is the family dog, but its mostly a girl and her dog with Avery. Although he was Tyler's wingman and vice versa. Just so we're clear, a talking dog put up with the annoying female dog of a hot girl his owner likes and later makes Tyler go on a date with a very annoying girl with a poodle that Stan likes. Hilarity Ensues.
Jessie: A boy (Ravi) and his lizard (Mr/s. Kipling).
The dark comedy/horror Tabletop GameMonsters And Other Childish Things puts a twist on this by making it A Boy and His Dark and Malevolent Forgotten God/Reality-Rending Extradimensional Horror/etc., rather than the relatively cute and benign monsters that are the standard when monsters are used in this plot.
A number of archetypes in Big Eyes, Small Mouth feature a hulking animal sidekick of some description. The Monster Tamer would be the standout, however.
The original games, on the NES and the Game Boy, had more of a sillier, irreverent tone than a traditional "boy and his x" work. The Wii Revival, on the other hand, was deliberately designed to milk this trope for every last heartwarming drop. How many games can boast a dedicated "hug" button?
Even worse, imagine some of the sharper ones poking you.
In Fallout 3, President Eden's radio messages frequently mentions his childhood, when he and his dog roamed and rambled. Subverted somewhat when it turns out President Eden is actually an insane AI and never actually had a childhood.
"A boy and his dog" fits the Lone Wanderer pretty well though.
In fact, according to Word of God the whole Wasteland and Fallout sagas are based basically half in the Mad Max universe and the other in A Boy and His Dog, with the latter even "approved" by the grumpy "if you steal from me I will sue you!" Harlan Ellison, since he is friend with some of the boys from the staff of Black Isle Studios/Obsidian Entertainment from long time ago
Also, every other Fallout protagonist may fit this trope.
The Vault Dweller from Fallout 1 has the ability to recruit the first Dogmeat in the series, a dog from a town close to Vault 13 and one of the first to visit (and, by canon, he did).
In Fallout 2 the Chosen One can recruit K9 (no relation with the Doctor Who character) or Robodog, two cybernetic dogs (and, Word of God, he did) He can also recruit the same Dogmeat from the first game again (although the dog died according the canon events that took place in Fallout 1), but this is only through a rare special encounter (Cafe of Broken Dreams) which is more an easter egg/joke for all the fans of the saga. Oh, and there is Pariah, another dog companion from a special encounter (A lone surviving dog), but this one is "jinxed" (intentionally in-game, but also buggy in general) so is preferable to avoid as a team partner
In the aforementioned Fallout 3 the Lone Wanderer can recruit the second Dogmeat in the series.
The Courier in Fallout: New Vegas can get the optional quest of repairing Rex, a worn-out cybernetic dog, and traveling around with him. And there is Roxie, a female cyberdog, in the DLC Old World Blues.
The Courier can also travel with ED-E, a salvaged Eyebot built by the Enclave. In Lonesome Road, the final DLC of the New Vegas, ED-E becomes your sole companion, has a significantly large role and even engages in "conversations" with the Courier.
Playing Warhammer Online as a High Elf White Lion could lead to A Boy And His Small Albino Attack Lion.
The Maw is a Small Blue Alien and His Unstoppable Gelatinous Eating Machine. Despite the innate potential for it in that premise, it surprisingly ends without a turn for the dark: the game ends with Frank, the small blue alien, finally having to leave Maw as Maw becomes a living planet and then eats the camera.
Also, a girl and her from-the-future partner and possible love interest, a boy and his stolen-from-his-sister-chance-at-greatness, a girl and her giant, a man and his new love-interest, and a man and his stolen partners. A Master and his/her Servant.
Played with in Ōkamiden, which is very much a "Kids and Their Dog" plot - from the perspective of the dog. And he repeats the process whenever he parts ways with one kid and meets another, to boot.
In Castlevania: Lords of Shadow Claudia, the resident Cute Mute, has one in the form of the Black Titan a seemingly magically crafted sentient suit of armor, gift of her late parents. Since Claudia can't fend for herself alone in the Crapsack World she inhabits, and the Black Titan needs to feed on evil souls, the Titan keeps himself alive by dispatching Claudia's potential enemies. However the Titan is revealed to be made with the reanimated corpse of a mute assassin, seeking redemption by helping a girl with his same affliction, and growing fonder to her in time.
Broodhollow: A neurotic insurance salesman and his adorable bat.
Averted in HERO — though the cat initially appears to fulfill the role, it stays behind when the protagonist enters the watchtower.
In The Inexplicable Adventures of Bob!, Bob initially adopted the tiny Molly the Monster as a pet. He had no idea she would prove to be intelligent and grow to human size. He now treats her as a daughter. Molly now has her own pet alien tentacle monster, Snookums.
The Order of the Stick- A Halfling (or A Sexy Shoeless God of War (And Cooking)) And His Cat. Previously, A Powerful Old Man And His Cat (the same cat, in fact). Perhaps it's more A Cat and His Owners.
Lilo & Stitch: A Girl And Her Alien(s). In the original film, Stitch was adopted by her by pretending to be a dog.
The Backyardigans has quite a few examples: A Kangaroo and His Dinosaur (Austin and Boy in "Caveman's Best Friend," the ultimate example), a Moose and His Burro (Tyrone and Molasses in "Horsing Around"), a Penguin and His Bath Mitten (Pablo and Mitty in "Robin Hood the Clean"), and A... Thing and Her Dolphin (Uniqua and Sea Squirt in "The Great Dolphin Race").
Danny Phantom: Sam directly mentions this trope twice, once with "A boy and his snow beast." and another time saying the more common "A boy and his dog..." before following it up with "... Somehow, it's not supposed to be this weird."
Bradley Nowell of Sublime and Louie Dog, his dalmatian. Bradley wrote a song Lou Dog Went to the Moon. When Louie was stolen,Bradley was inconsolable. Laid on his couch for about a week and cried. He sand Lou Dog Went to the Moon into his answering machine. There are several songs that mention Louie Dog, including: Doin Time, Garden Grove/Garbage Grove, and What I Got. Bradley missed Louie Dog so much he had flown to the East Coast on the original Warped Tour. When Louie Dog died, several years after Bradley, the family buried a phial of his ashes with Bradley, and scattered the rest at the same surf spot they scattered Bradley's. To this day the band, now dubbed Sublime with Rome sells Louie Dog shirts at concerts.
A man and his horse. Viggo Mortensen has such a love for horses that he bought the two steeds he rode in LOTR and one of the horses that played Hidalgo. He also reportedly bought the stallion that played Arwen's horse and gave it to the stunt double.
Hachiko the dog earned fame in Japan for returning each day to the train station where his master last departed before dying. The Japanese people were so touched that they gave him a statue outside of Shibuya Station, exactly where he would sit.
Greyfriars Bobby was a constable's watchdog who lived in and around the graveyard where his master was buried for 14 years.
Michael Jackson was famous (and occasionally infamous) for his intense bond with a wide variety of pets, especially in his younger years. Rats, cats, dogs, even a chimpanzee. He reportedly preferred animals to people, having found in them a source of unconditional love and friendship that fame and family did not bring him.