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 (not to mention the fact that 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.
Shaman King: A Boy and His Six-Hundred-Year-Old Samurai Spirit.
The ADV advertisements for All-Purpose Cultural Cat Girl Nuku Nuku described it as "the heartwarming story of a boy and his cat... and a major military equipment manufacturer."
Code Geass: A Boy and His Witch. Lelouch himself says that he feels this way late in the series when C.C. asks if he regrets their meeting and the dark path he's taken as a result.
Lyrical Nanoha: A girl and her ferret in the first series; A girl and her Wolkenritter in the second. Lolis and their badass combat powers in both.
Fullmetal Alchemist A boy and his armor suit whose brother's soul in bound to said suit.
Brigadoon: Marin and Melan is a heartwarming tale of an orphan and the robotic living weapon that protects her. Depending on your tastes, it's either better than or weirder than you would think.
Not really a comic book (but there are books available): In the Berkeley Breathed comic strip Bloom County, the introduction of the penguin Opus quotes this trope. "A boy and his penguin. A penguin and his boy"... Of course, then the dad has to be sarcastic about it and add his own variation: "Two dips and a dad." The trope is not followed, however, as Opus becomes more and more neurotic, and less and less a side kick.
In X-Men comics, 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."
Another X-Men example, of course, is 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 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.)
Used in Marvel's What If? series in the story "I'll be your best friend!". The cover declared that the story starred "Cannonball's little brother Josh... and his pet Sentinel!"
Yet Another Boy and His Sentinel: Tom Skylark and Rover in the "Here Comes Tomorrow" storyline in New X-Men.
A Boy and his 'Bot by Gary Thomas Washington.
C.O.P.S. #5 centered on Bowser and his cyborg dog Blitz, and Bowser/Rex Pointer's memories of his first dog, Maxie.
Free Willy: A story about a Boy and His Willy. Sorry, a Boy and His Relationship With His Little Whale. No, wait, a story about a Boy Who Likes To Hold On To His Big Fish. Uh, a story about a Boy and His Killer Whale. No, no, a story about a Boy and His Orca. There we go!
Hachi: A Dog's Tale: A professor and his dog, which is based on...
The French film The Fox and the Child: A Girl and Her Fox.
Played straight in Disney's "Homeward Bound" films (a boy and his dog plus a girl and her cat). Though most of the time it works the other way around, a dog/cat and their boy/girl.
The Beastmaster: A man and his Panther, Eagle, and two Ferrets.
Ted: A boy and his teddy bear, who comes to life. But what happens when they grow up?
Literature
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.
Interestingly played with in The Never Ending Story, where a Boy and His Horse relationship is early driven to a moving end... only to be replaced with a better partner, when The Hero finds a much more interesting companion, turning the trope into A Boy And His Dragon (and Dragon Rider, incidentally).
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 to hell: 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.
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.
Given that it's usually young-ish teens who Impress, the entire premise of Anne McCaffrey's Dragonriders of Pern is basically a Boy/Girl and their Dragon.
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, 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 books. The Circle of Magic has A Boy And His Plants, A Girl And Her Starling, and A Girl And Her Magical Glass Dragon. The last one 'breathes' flame-shaped glass ornaments.
Walter Farley's The Black Stallion series is very much A Boy And His Horse. So was his Island Stallion series.
Clifford the Big Red Dog: A Girl and her gargantuan dog. One of the songs on the tribute album for the Scholastic animated series is titled "A Girl and Her Dog."
Edgar Pangborn, "Tiger Boy". The wandering youth seems kind and gentle but lets his tiger perform euthanasia on the old and sick. This leads to a tragic ending.
His Dark Materials has elements of "A Girl and her killer sentient metalworking badasspolar bear" to it, but as people are born with part of their soul external in the form of an animal-shaped daemon, it also has this as the basis for most of their entire society.
Bloom County: A Boy and His Penguin. (Originally. This angle was swiftly dropped when Opus became the Ensemble Darkhorse.)
Binkley Jr.: I for one think it's uniquely wholesome. A boy and his penguin!
Opus: A penguin and his boy!
Binkley Sr.: Two dips and a dad.
Tabletop Games
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.
Video Games
One Xenosaga4-koma aptly sums up the series as "A Girl And Her Doll". Of course, said "doll" is a combat android with the power of a fleet....
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.
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).
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.
The Courier may also travel with ED-E, a small robotic sentry acting as a floating R2-D2.
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.
Before that however, there's Mega Man Battle Network, about a boy and his PET ("P-E-T", or PErsonal Terminal, his artificially intelligent, cell phone/computer thingy).
Who happens to be his twin brother.
In the original game, Megaman and his red robot Rush.
In later games in the original series, Bass and his purple robot wolf Treble.
Guardian's Crusade has a boy and his baby dragon. Emphasized since you have to take care of it and treat it right, so the attachment can extend to the players.
In Final Fantasy V, Faris and Syldra are a "Boy and his Dragon" except later the hero discovers that Faris is actually a girl crossdressing.
Team Ico Series have this in all of their games (as of yet):
Ico: A boy and his... Yorda? Though she is a human girl you interact with her like she was a pet who you can hold hands with a lot.
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. Basically, a Master and his/her Servant.
Played with in Okamiden, 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 basically 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.
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 His Cat. Previously, A Powerful Old Man And His Cat (the same cat, in fact). Perhaps it's more A Cat and His Owners.
In Survival of the Fittest, Cody Jenson, the villain of V1, has this with him and his bike. However, instead of starting him down the path to manhood, it starts him down the pathtoinsanity.
The Nostalgia Chick has this complaint about Dragonheart and other dragon movies, seeing as how most girls loved dragons (or at least she did) and women never factor in the films.
Western Animation
Code Lyoko: A boy and his dog. Odd and Kiwi (who isn't supposed to be in Kadic)
Dreamy Dud: A boy and his dog. First animated example (1915).
Bobby Bumps: A boy and his very cynical talking dog. Second animated example (also 1915), but started earlier as a (slightly differently named) comic strip.
Dinky Doodle: A boy and his humanized dog (1924), living with the cartoonist that created them (so also "a cartoonist and his cartoon wards").
Sammy And Sausage: A British boy and his British humanized dog (1928), living with the cartoonist that created them. Rather transparent foreign Expy of Dinky Doodle.
Mickey Mouse and Pluto: A boy (mouse) and his dog. First Funny Animal character to regularly own a nonhumanized animal as a pet; ribbed about it to this day.
Adventure Time: A boy and his magically shapeshifting dog friend.
Avatar The Last Airbender: A Boy And His Flying Bison And Flying Lemur. Also mentions two separate instances of A Man And His Dragon.
Lilo and 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."
Teen Titans: A girl and her mutated silk worm. Though at first it was a Beast Boy and his mutated silkworm, it appears Silkie grew more attached to Starfire in later episodes.
Jimmy Neutron has Jimmy and his mechanical canine, Goddard.
Parodied in The Simpsons with Soccer Mummy, a film within the show in which a reanimated Egyptian mummy joins a little league soccer team and teaches a young boy to believe in himself.
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. Literally, 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.
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.