Pops up a few times in Cinderjuice in regards to Beetlejuice and Lydia. Donny, BJ's brother, outright calls himself this in regards to the pairing. He's joined there by Prince Vince and Lydia's friends Prudence and Bertha, and... pretty much everyone who knows them, really.
In The Fledgling Year, many of the girls who are supposed to be Cor’s potential brides dont bother trying to ingratiate themselves—not because they don’t like him, but because it’s obvious to everyone but him that he’s in love with Aravis. Hana particularly outright says that it’s ridiculous to think of anyone but Aravis marrying Cor, and periodically gives her advice on their relationship.
In her first appearance, Beth believes in the Doctor's love for Rose Tyler and uses it to help bring the Doctor back to himself.
Later on, Beth is an all-out shipper for Watson and Sally, realizing that Sally is the mysterious second Mrs. Watson of the Sherlockian Canon and thinking of the newlyweds as the cutest thing ever.
Sally, in turn, fully supports Beth in her love for Holmes and practically squees when she sees the two of them married and simply acting like newlyweds.
The Doctor ships both Watson/Sally and Holmes/Beth, although he's more active in encouraging the latter.
Played for Laughs in Fly Free, where Sakura is convinced that Robin and Kakashi are meant for each other. Other characters, including Ino, Naruto, and Sasuke are convinced by the 'proof' that Sakura shows them.
Misato shipped Shinji and Asuka and tried to help them to get together.
Shinji also shipped his friend Touji with Hikari.
Misato shipped Shinji/Asuka in Children of an Elder God. In a scene she asks if they’re making out, and when they deny it, she pouts.
Last Child of Krypton: Misato shipped Shinji and Asuka even before both teenagers met. When she and Shinji were going to pick Asuka up from the airport she talked at length about Asuka, assurring Shinji that he'd like her a lot.
In Beyond The Outer Gates, a crossover between The Dresden Files and High School Dx D, Lash strongly supports Harry in romancing both Sona and Tsubasa, gleefully encouraging him to start a harem. This gets even worse in a continuation fic by a different author that adds Reya and Serafall to the mix. Harry himself is romantically interested in all the girls, but is hampered both by his mental age (he arrived in the Dxd world in a teenage body but retains his original mind from when he was well into his 40's) and his previous relationship history.
Later chapters of the continuation fic implies that the Winter Mantle also pushes for Harry to hook up with the girls, despite not technically being a person of its own.
As for Watari, he's implied (mostly in supplementary material) to have shades of this himself. However, unlike Misa he never says anything about it nor does he act on it, chiefly because A) L doesn't need the distraction, especially not while he's working on the most dangerous case he's ever taken up, and B) he figured nothing would have come out of it anyway just because of how L is. He prefers to leave it to L to ultimately make his own choices. He doesn't live to see for himself, but he was right.
"Do you know how many tires I had to slash, how many boys I had to threaten, how many dates I had to turn down just to make the way clear for the two of you to finally see each other for what you were? Half the fights I got into at school in some way involved you lot. But that's ok, that's what I wanted. The two of you belong together and not just because it was necessary to maintain the timeline, complete the paradox and create me, but because you truly love each other."
In Shadow And Rose, Leliana is a confirmed Alistair/Warden shipper from a very early point in the story. Wynne eventually joins her in this; most of the others just sort of roll their eyes.
A lot of the background characters are this for the two main pairings in All This Sh*t is Twice as Weird, with Varric and Dorian leading the shipping squad. The two main characters also very much ship one another with their respective love interests.
In Age Of Dragons Lenore Amell is this for most of her friends. Later, Lenore and Dorian bond over how adorable they think Cullen and the Inquisitor are together. Isabela is a dedicated Hawke / Fenris shipper, though she often playfully ships herself into their relationship.
In the Fallout 3 fan fiction Trouble, Johnny Saint the legendary vault dweller can see the chemistry going on between Harkness and Butch, and casually offers Harkness advice on how to deal with Butch's emotions.
Lissa and Sumia support Frederick/Robin after realizing the two are spending a lot of time together in Pretender. Justified in Sumia's case, she knows that Robin has feelings for her husband Chrom and hopes that if Robin moves on, Chrom will stop being obsessed with Robin.
Lucina Reacts: Everyone, for everyone- or rather, almost everyone for almost everyone. For specifics:
Almost everyone for Lucina and Robin, although Sumia and Reflet are the primary shippers apart from the Cabal. Sumia's true motive is revealed, while Reflet's is far more altruistic.
The Justice Cabal drives most of the shipping. Their primary targets are the above Lucina and Robin, Lon'qu and Cordelia (although they were revealed to have been an Official Couple long before the story began) and Gangrel and Emmeryn.
Pretty much everyone in the Elemental Chess Trilogy is a Shipper on Deck for Roy Mustang and Riza Hawkeye, though probably no one more than Grumman. Flashbacks in the second story and several incidents in the prequel indicate that the shipping has been happening for years.
Lereal Belsai, the Sufferist leader in Hivefled, was horrified to find that Nepeta broke up with Karkat when her kismesissitude with his best friend Sollux got in the way, as he thought they would follow in the footsteps of their respective ancestors. Nepeta, the Homestuck canon's resident Shipper On Deck, is horrified by his idea of her and Karkat being in a relationship which transcends the quadrants; not only does she not want to be left without her kismesis and moirail, but it would make her own shipping wall a lot more boring. Gamzee, meanwhile, becomes a Shipper On Deck for Feferi and Sollux's moirallegiance, fearing that he will be stuck with Feferi in a Pair the Spares situation and repeat the relationship of their ancestors. (Their shared ancestors, to be specific. Moirails reproducing is a taboo equivalent to human incestuous reproduction, but Condesce and the Grand Highblood did it anyway.)
Nepeta'sshipping wall and ways are Deconstructed in Be the Sea Dweller Lowblood, where she's oblivious to Eridan's flushed feelings for her and tries to set him up with his moirail Feferi. This eventually leads to her discovering that she doesn't understand Eridan enough to be a true moirail, while Feferi is not pleased with Nep seemingly trying to steal her moirail away, and just how manipulative and controlling this makes her appear to them.
There are multiple Shippers on Deck in Some Semblance of Meaning: Fen implies that she wishes Vale had been born in District Five so she and Fen's brother Lark could have gotten together, whereas Vale's sister Laurel is shown to be a wholehearted supporter of Vale/Obsidian (and she's not alone).
Many fanfics have the characters (Kim and Ron's parents and the kids in school) be this for Kim and Ron, even before they were an Official Couple. It was also acknowledged that some assumed that they were already a couple beforehand.
In Where The Eyes Of The Old Gods Can't Hope To Find Us, Kenzi (as in the show) ships Dyson/Bo despite Bo dating Lauren. Deconstructed when Lauren calls her on it, by pointing out how that makes her feel. In fact, as Lauren points out, everyone ships Bo with someone other than her. Trick, Kenzi, and of course Dyson himself all want her with Dyson. Hale wants her with a Light Fae, to sway her into joining the Light.
Deconstructed in Perfection Is Overrated, in which Bachiko, as well as her accomplice Meiko not only has the opinion that certain characters would be better off with other people, but as a SUE, has the power to make those desired couples a reality.
Played straight with how Isana supports Nagisa and Keitaro getting together after noting how close they've become.
Deconstructed with Mutsumi who wants nothing more than to help Naru and Keitaro hook up. Too bad this means constantly ignoring Keitaro's insistence that he doesn't want anything else to do with the violently abusive Naru. Her continued attempts to 'help' completely destroy their friendship.
Rich Bitch Kagura is a rare villainous version: she specifically wants Nagisa and Keitaro to get together so it'll be even more painful for Nagisa to lose him.
Earth and Sky: Rarity plays matchmaker for Applejack and Soarin' and Apple Bloom and Pipsqueak, and takes things to almost Chessmaster levels of planning.
The Elements of Harmony and the Savior of Worlds: Applejack and Mike actively try and play matchmaker between Fluttershy and Big Macintosh (AJ's actually been trying for years, hampered by Fluttershy's shyness and Big Mac not feeling good enough for her). Granny Smith eventually gets in on the act, complaining that the two of them have been laying it on too thick.
Big Mac appears to be this for Caramel (Big Mac, AJ and Applebloom's cousin in the fanfic) and Blues Noteworthy.
Rarity, and to a lesser extent Rainbow Dash, decides to help things along between Fluttershy and Pencil Pusher in Flash Fog.
Spike becomes this in parts of It Takes a Village, first prodding Fluttershy and Big Macintosh together. In the epilogue he's finding a new date for Rarity and also working on getting together Pinkie Pie and Caramel.
In Magnetism, Rarity apparently starts shipping Fluttershy and Rainbow Dash after hearing about their awkward bath together.
Apparently is replaced with blatantly in the last chapter when she and Pinkie try to erect a banner with Fluttershy and Rainbow Dash's face with a heart between them outside the Golden Oaks Library. Applejack, however, talks them into taking it down before either shipped pony can see it.
In The Melting Pot, a good part of the action is set off by Pinkie Pie telling Lyra and Bon-Bon they make a cute couple just before going on a trip. In the final chapter, Pinkie turns out to be subtly setting up several budding romances between background characters from the show.
It's shown during Shining Armor's flashback arc in the Pony POV Series that Cadence's hoofmaidens and at least some of Shining's squadmates shipped the two of them prior to their getting together. And they weren't subtle about it. At all.
Shining and Cadence themselves both get their own, more mild, examples of this — Cadence is working with the hoofmaidens to set up Private Running Gag and Private Garnet Chambers, while Shining has said on a couple of occasions that Captive Audience is the stallion he feels would be the best match for Twilight.
Taken up to eleven in with Rarity in the fanfic Shipping Goggles. Rarity apparently has a pair of the eponymous goggles welded to her head, as even the most innocent of interactions is treated as prime shipping fuel by the white unicorn, much to the frustration of Twilight, who can see Rarity shipping their friends.
In the Ponies Of Olympus series, as revealed in Atlas Strongest Tournament, Sweetie Belle ships Spike with her sister, while Apple Bloom ships him with Scootaloo.
The Nuptialverse: A Running Gag in Families is that Pinkie Pie is convinced that Applejack and Twilight are in denial about their true feelings for each other.
Pinkie Pie and Fluttershy for Applejack and Rainbow Dash in Morning Glory. They slip them the Apples' "honeymoon cider" which was meant for Fluttershy, not that she needed it.
Parodied in Tealove's Steamy Adventure. Big Jim the cave troll captures the ponies and treats them like toys. This includes shouting "SHIP PONAYS!" as he picks up Tealove and Snowcatcher, then tries to make them kiss. The other pony, Libra (who's not entirely right in the head), immediately agrees that they have such great chemistry together.
This is the entire premise of the fanmade card game Twilight Sparkle's Secret Shipfic Folder. There's also an expansion pack which makes Discord the author instead.
In Naruto Veangance Revelaitons, an odd variant of this happens when Ronan's girlfriend Sakura, meets Atni for the first time (While Sakura was dead after being killed by the Council, Ronan met Atni and had sex with her several times).
Sakura: OMG WHO IS DIS WHOT BITCH CAN U FUK HER/"
Tsunade and Hanabi ship Naru Hina in A Growing Affection. Tsunade offers to train Naruto and Hinata together, partly to help them get stronger, but also to give them a reason to spend time together. Hanabi is more than willing to run interference for Hinata with their family, at least until she gets angry at Naruto for an unrelated incident.
Kushina in New Chance. Considering how when she died she became a ghost that hovered around Naruto until Time Travel and a resurrection happened, she tries to make him happy and thusly ships Naru Hina. To an unhealthy degree. If Minato wasn't around reminding her the two are only 12 and stopping some of her more blatant or outlandish attempts to get them together, she'd be giving both a Shotgun Wedding.
Ino actively ships Naruto and Hinata, even playing The Matchmaker to get the two of them together. Kabuto and Sasuke likewise approve of the two becoming an item, with Kabuto setting things up so Naruto and Hinata will dance together at the Hyuga family's annual ball, and Sasuke remarking, on seeing them dancing, that they look good together.
Both Hinata and Minato pair Yugito with Itachi; Hinata says at one point that she'd like to be the maid of honor at their wedding, and Minato frequently drops hints that Itachi should pursue Yugito.
Itachi seems to approve of Sasuke being with Sakura, at one point suggesting to his brother to ask the pink-haired girl out.
Of The River And The Sea has the Mumei, who are quite invested in the relationships between the Kiri no Kaijuu and how it will pan out. Beyond that, Haku ships Zabuza/Ryuishi because they're basically his parents, Itachi - by Word of God - ships Kisame/Ryuishi because they were the only ones to have sympathy for him after the massacre, Sakura ships Kakashi/Ryuishi because she thinks it's so romantic and Hanako ships Zabuza/Kisame because she outright worships Ryuishi and doesn't believe in Divine Date.
On a more serious note, the Hidden Mist would like to use Ryuishi's political, social and economical influence and power, which could be attained by marrying her to a high-ranking, loyal Kiri operative. Such as Zabuza - one of the Seven Swordsmen - who happened to be very close with Ryuishi.
Misato shipped Shinji and Asuka together (the fic started as an one-shot story where Misato encouraged Shinji to win Asuka over and gave him tips). Kaji also ships them together. The hilarious part is how Shinji and Asuka are now acting as they used to and leaving them to just assume that the pilots are still deep in the Belligerent Sexual Tension phase, when they are in fact very together.
Rei turns this Up to Eleven. To her, Shinji and Asuka's romance is the single most beautiful thing in the world, and she would do anything to make sure that they can be happy together. Merely implying that you might be a threat to that is a Berserk Button for her (as Kaworu quickly found out).
Shinji and Asuka also ship their best friends Touji and Hikari. And after getting over her crush (in part thanks to Shinji), Asuka encouraged Misato to going out with Kaji. And then the two of them toy around with the idea of shipping Rei with Kaworu (after making sure that he isn't a SEELE spy).
Misato also ships Shinji and Asuka, although she'd settle for them learning how to get along well.
Nobody Dies: Rei was apparently shipping Shinji/Asuka ten years before the three of them even met each other. She also somehow hooked up Toji and Hikari during the unseen Third Angel fight, and now claims to be shipping Shinji/Asuka's and Toji/Hikari's hypothetical future children. This seems to be a universal trait among the Ree (they all ship Shinji/Asuka, except Zyuu, who wants Shinji for herself), and Lilith herself seems to ship everyone/everyone as part of her desire for babies.
Once More with Feeling: Shinji tries -and manages- to hook up Touji and Hikari. He also tries to set Rei up with Kensuke. Kaji also gives tips to Shinji for winning Asuka over. In addition to these straight examples, there's an interesting inversion: Obviously Shinji is not against Kaji and Misato hooking up, but after telling Kaji how his death left Misato devastated in the original timeline, Kaji decides to stop flirting with her until the Angels, Gendo and SEELE are defeated and dead.
Misato is a Shinji/Asuka shipper. Ironically she doesn’t know that they already got together.
Hikari tries to hint Shinji that Asuka likes him. Ironically she doesn’t know that he’s quite aware of it since he's her husband.
Shinji and Asuka ship Touji and Hikari -and played matchmaker for them successfully-, and they secretly ship Misato and Kaji.
For a time in Neon Metathesis Evangelion, Asuka shipped Shinji and Rei together, partially because all three have feelings for each other and she wants to solve her dilemma by pairing them up so she can bow out.
In One Year, Hitomi ships Yu Narukami, one of her old friends, with her best friend, Sakura Takahashi, to the point at which this is one reason Hitomi doesn't go after him herself, the other being that she's in an Arranged Marriage. Unfortunately for Hitomi, Yu fell in love with Yukiko while he was in Inaba, and so has to turn down everyone else.
Lilia from the remakes of Pokémon Ruby and Sapphire returns in Dating A Team Magma Grunt and is introduced by Brendan to his girlfriend. While it is tame at first, and she admits her plan to get the Magma and Aqua Grunts to compete in a competition for Brendan was more out of hosting a contest with more participants rather than shipping him with a specific girl, she's clearly loving the moment he and the Magma Grunt share their first kiss.
Eventually in Old West, Priscilla asks Teddy if his mother Grace is going to be married with Rattlesnake Jake. Having never had a father for his entire life, the boy finds himself liking the idea of his loving mother and the outlaw he admires together and starts getting ideas on how to make that happen.
"PYRRHA'S SMOKIN’ HOT AND SHE’S IN NOTHIN’ BUT BOXERS AND A TANK TOP." Yang crowed as Blake wolf-whistled. "BOY IS SHE FIIIIIIIIINE."
"I will kill both of you!” Pyrrha snapped as she covered her phone. “With my bare hands!”
RWBY: Reckoning has Blake and Ruby supporting Yang and Darrel's attraction to each other. Blake outright states that the two would make a cute couple.
The fic Matchmaking Madness has all of Team RWBY as this for Jaune and Pyrrha; all four of them attempt a Zany Scheme to get the two to hook up. While all of their attempts fail, the two still end up becoming a couple, thanks to the efforts of Cardin, who happens to be this for them as well.
Weiss Reacts has Yang for Ruby and Weiss. Due to the events of the Music Festival, the pair becomes a reality as of chapter 72 of Volume 1.
Exaggerated in the fic Team RWBY: Master Matchmakers, where Ruby is so hell-bent on getting Jaune and Pyrrha together that she convinces the entire student body to help her.
Weiss very much ships Ruby with Aero in Shard and isn't to happy with the failed attempts to push them together during the day at the beach chapter.
The RWBY Loops has Ruby react to any ship with glee, so long as it doesn't involve her. It's implied she does this mostly to combat her own loneliness during loops where nobody else is present, and generally avoids causing issues for actual relationships.
Most of the humour in the fic Written In The Stars (in which the Kirks of both realities have been genderswapped) comes from Kirk Prime trying to get her counterpart to hook up with Spock. This is justified in that Kirk Prime and Spock Prime were married in their own reality, and Kirk Prime just wants her counterpart to be happy. She succeeds.
The Wrong Reflection has Eleya's family, for her and Gaarra. Note that at this point Eleya and Gaarra are already together, but they're keeping the relationship a secret for legal reasons.
Kanril Torvo: So, when are you two getting married? (Spit Take from Eleya)
In Things We Don’t Tell Humans, Optimus Prime is this for Bumblebee and Barricade, and perhaps for Sam and Carly, too. Jazz and Prowl have a whole fleet of shippers, consisting of their son, Jazz’ parents, Ratchet, Optimus and Elita, Megatron, Terratron, and likely more. Prowl, in turn, ships Ratchet and Wheeljack.
In the Black Crayons series, Annabelle Lennox is waiting rather impatiently for Ironhide and Chromia to realize they belong together.
In Ripples, Queen Weira is shown to constantly be hoping that Phobos and Van will have a Relationship Upgrade, even at one point mentally referring to the latter as her "future daughter-in-law".
The Gaang Jr. fan-project gives us Yi Lin, a walking riff on the Avatar fandom's shipping community. She's obsessed with other people's love lives and hides all her collected "Proof" in a book supposedly about...well, ships. She's a Tyzula fangirl in particular, although she can't get other people to see it (and if they ever do see it, they're not going to tell her since it would just make her harder to live with). Fittingly, she refuses to see that there's something going on between Irah and Hayoda.
In the Axis Powers Hetalia/Ace Attorney crossover Turnabout Hero, Hungary seems interested in shipping Edgeworth and Phoenix. At one point, she even snaps a picture of them sitting together and thinks it's cute. Given that it's Hungary, no ones surprised.
In the Fire Emblem Awakening fic Lucina Reacts, Morgan and Sumia ship Robin with Lucina. Morgan also ships several other couples, including Lon'qu and Cordelia, and seems to be aiming to ship everyone with everyone at some point.
In the Hey Arnold! fanfiction Oh Rhonda, Phoebe and Nadine like the idea of Rhonda having a crush on Arnold and try to push them together as best as they could. Likewise, Rhonda and Nadine ship Phoebe with Gerald.