All of the Aizawas in Aizawa San Multiplies are pushing Shino Aizawa and Souta Mizutani together. Notable in that four of the five Aizawas outside of Shino thus far introduced are Literal Split Personality manifestations. In their case, it's justified by the fact that, when they remerge with Shino, they get all her experiences as if they got it - Souta effectively dates five girls at once.
Ashita no Nadja: Nadja Applefield ships Sylvie/Raphael. Sylvie, in return, ships Nadja/Francis, though she's more aware of how Love Hurts...
Marianne Hamilton ships Nadja/Keith, since she's got a crush on Nadja's love interest and Keith's younger twin brother Francis and having Nadja go the Settle for Sibling route would let her have a chance with him. She even admits it to Nadja herself in one of their talks.
Julietta is a subversion, as when Nadja is caught with her feelings for Keith and Francis, she tells Nadja "choose the guy YOU want and not the one you feel obligued to love back" but doesn't explicitly show preference for either of Nadja's love interests.
Karma, being Nagisa's self-appointed wingman, has taken pictures of every kiss he's ever had. That said, he goes to great lengths to encourage Kayano specifically to kiss him again- even staging a reconnaissance mission to reassure her Valentine's Day jitters.
Reiner from Attack on Titan seems to be this for Bertholdt and Annie, as he pushes Bertholdt to confess to her once they return home.
Japan of Axis Powers Hetalia may count. When Italy asks for advice on a designing a war poster, Japan suggests putting Italy and Germany's names under an Umbrella of Togetherness. Austria also gives Germany dating advice in the Valentine's comics.
In fanfiction and fanon Hungary definitely takes on the role of whoever is getting together in that fic. E.g, in a lot of a fanfiction this troper's seen Hungary (due to her status as yaoi fangirl) has openly shipped Amercia and England, Sweden and Finland, and Germany and Italy being the big one due to her involvement in Italy's past. Also in some fanfiction, North Italy may take on this role as well but this doesn't happen as often.
Maylene from Black Butler gets nosebleeds every time Sebastian makes a... comment where the meaning is ambiguous to Ciel, despite having a crush on him herself. She's probably just a Yaoi Fangirl though, and in another instance, when she thought that Sebastian was the one Ciel liked the most, she got noticeably jealous and coined Ciel as a possible "love rival".
In the Blade anime, Wolverine gets the idea that Blade and Makoto should be a couple. They vehemently deny this.
In Bleach, the manga periodically has different characters addressing the idea of Ichigo and Orihime:
In Candy Candy, Candy ships Annie Brighton and Archie Cornwall after learning that they have a Long Distance Relationship. Things get complicated when the three arrive to the same Boarding School and it turns out Archie has a crush on Candy, which triggers Annie's insecurities. It's resolved relatively soon, however, and Annie and Archie officially get together.
Captain Tsubasa: Pretty much the whole Nankatsu JHS Soccer Team (their Team Dad doc included) ships Sanae/Tsubasa. Evne Kumi, Sanae's love rival, joins the group without any misgivings or reservations after Tsubasa turns her own confession down.
The kids in the Furano team ship Yoshiko/Matsuyama. The Team Mom assistant and the Team Dad captain... perfect!
Tomoyo Daidouji ships Sakura Kinomoto and Syaoran Li.
In The Movie, Meiling Li, Syaoran's cousin and ex-fiancee, helps Tomoyo to try and get Sakura and Syaoran together.
Kaho Mizuki is a Touya/Yukito fangirl from before Touya and Yukito met. For added effect, she was dating Touya.
Captain Kuune in Cat Planet Cuties seems to ship Eris and Kio- she arranges for Eris to attend school with him and sets up other opportunities for the two of them to spend time together in order to give them romantic opportunity. She doesn't do anything to try sabotaging Kio's other two potential romantic partners. Possibly because polygamy is the norm on Catia (due to there being roughly a 20 to 1 ratio of females to males there), she's just trying to make sure that Eris is included in the relationship.
In Charlotte, Mishima for her friend Yumi towards Yu. After he's invited for some pancakes, she pretends to suddenly have to go home so the two can spend time alone together.
The Amakusa are all for one of their own, Itsuwa, snagging The Hero Touma Kamijou. They try to arrange things to help Itsuwa out and tend to get frustrated when her shyer tendencies cause her to be too passive.
Pretty much every girl in the series has friends who are trying to get her together with Touma. Mikoto is one of the few who gets shippers outside her social circle; at one point the president of the United States encourages her to confess her feelings.
Kaguya ships Lelouch with Kallen and CC, along with herself, as his personal harem.
Asahina ships Todoh / Chiba, suggesting that Chiba "confess already" early in Episode 5 of R2, and his comments about Chiba having a reason to live on after saving her life in the second battle for Tokyo causes her to blush, indicating she knows what he's implying.
And Lelouch seems to ship his best friend Suzaku with his little sister Nunally, or at least consider him good enough to to protect her. Naturally, this goes to Hell afterwards.
While Conan is generally very snarky in regards to romantic love, he seems to support match-ups if he truly thinks that the ones who could hook up will be happy, and therefore he ships Takagi and Sato as well. One story had Sato promise to marry her co-worker Shiratori if Takagi doesn't come to her by a certain time. While Takagi really and truly wants to get to her, he's held up by a very confusing murder mystery he's gotten caught up in; Conan gives him some help on the case and, when it looks like Takagi's not going to make it in time, sets up an illusion that he's there, giving the real Takagi the few extra minutes needed to make it.
And on the other other hand, Sonoko was very reluctant to ship Ran and Shinichi, since she believed (and still sorta believes) he's not good enough for her. In one of the OAV's she even urges Ran to go out with Dr. Araide... Thank God it's All Just a Dream. She loosens up with time.
Sato and Takagi themselves ship Kobayashi and Shiratori, specially Sato. One can pass it up as them being relieved that Shiratori isn't interferring anymore, but they seem to be genuinely fond of the idea during the mini-arc focusing on them...
Sato [in a VERY giddy, almost Genki Girl-like tone and attitude]: "Sooooo, where's the cute teacher that Shiratori-kun is so in love with?! Huh? Huuuuuh?!"
Kazuha and Heiji also ship Shinichi/Ran. Heiji, as one of Conan/Shinichi's secret keepers, has openly told him to just tell Ran about his secret identity so she won't suffer anymore for his "absence". On the other hand, even when Kazuha's father Ginshirou Toyama can be veryoverprotectiveof his little girl, he has also implied that Heiji is pretty much the only potential boyfriend of hers that he would approve of without any reservations.
Shinichi's almost child-like mother Yukiko ships her son with Ran. She has referred to her as "daughter in law" at least once, and has also teased him about it.
Interestingly, she also ships him with Ai/Shiho.
Aoyama lampshades and spoofs the trope once. Ran says that Conan and Ai are very cute together, Sonoko retorts that Conan and Ayumi are cuter, and they almost get in a verbal spat for it.
Erika: Hey, Shizu-chan must like Iza-Iza a lot, right? Kind of like Boys Love between two guys? Walker, Kadota, and Celty:No.
Shinra may also ship Shizuo/Izaya, given that he begins to consider the possibility of there being something between them before being cut off by a horrified Celty.
And surprisingly, Izaya is a Shinra/Celty shipper but this only applies to Shinra's side because he won't hesitate to mock the two whenever Celty is nearby. The Valentine's day comic proves though that he does care for Shinra if he's willing to put up with his spazzing about the holiday and give him actual advice without asking for money or trolling him afterwards.
Happy likes to ship anyone who has feelings toward others, mostly Loke/Lucy. In fact, he ships just almost anybody, Gray/Lucy, Gray/Juvia, Ren/Sherry and Daphne/Gray. He usually says "He/She liiiikesss you" whenever this happens.
Virgo does this as well, towards both Gray/Lucy and Natsu/Lucy, and using Happy's catch phrase.
Lucy flipped this back to Happy by shipping him with Carla.
Juvia is a fan of Natsu/Lucy, though that's probably because it means less competition for Gray's affections.
Mirajane told Lucy about Natsu having feelings for her, which she denied, resulting in many fantasies about being with Natsu. It continued when Mirajane told Lucy that Gray has feelings for her.
Gildarts ships Natsu with Lisanna.
By the end of the Nirvana arc, Natsu ships Jellal/Erza. "You have to stay by her side!!" indeed.
Ultear seems to ship Jellal/Erza as well. She questions Jellal's choices after he turns Erza down. And when Merudy asks why Crime Sorciere needed to meet Fairy Tail before the Grand Magic games, Ultear explains that it was important for Jellal/Erza. This is somewhat justified, considering she's the reason they aren't together.
With Elfman/Evergreen Ship Tease picking up, Freed and especially Bixlow have begun shipping the two.
Erza encourages Gray to tell Juvia how he really feels about her.
MayukoShiraki is the Shipper on Deck for her best friend Kanna and her crush/cousin Hatori. Years after it all goes horribly wrong, she still feels guilty for taking Kanna's place in Hatori's affections.
Momiji ships Kyo/Tohru, despite having a crush on Tohru himself. In the manga, it's his warning to Kyo about the Green-Eyed Monster that makes him face his own feelings for her.
Kakeru ships his friend Yuki and his half-sister Machi. When he points out to Komaki that the two have a thing for each other, she also seems rather pleased by the idea. And while Ayame takes a minute to catch on ("why would you go gaga over [Machi]?") he quickly joins in on the shipping as well, trying to get her to dress up in something cute for Yuki.
Nothing pleases Tohru more than learning someone she cares for is in love, and she ships for all she's worth.
Tohru's friends want nothing more than for whoever she dates to be a nice guy who appreciates her. So while they are extremely pissed at Kyo for rejecting her and refuse to let him visit her in the hospital because she's still upset, they do tell him later that they know he's a good guy and to please be good to Tohru. Tohru's grandfather also seems to approve of Tohru/Kyo, noticing that his granddaughter means a lot to Kyo; because of this, he tells Kyo about Tohru and Kyoko's rather unpleasant relationship with the rest of the Honda family, especially after Katsuya's death. (Before this, her grandfather was also the only relative who supported Katsuya's marriage to Kyoko.)
Kaname's best friend Kyoko ships Kaname/Sōsuke like crazy. She does everything she can on Kana's side to get her to like him (including making teasing comments to make Kaname realize her feelings for Sōsuke, which more often than not actually does work). Exactly why she would want to pair her best friend up with the violent sociopath that is constantly bombing and shooting around the school for outlandish reasons remains a mystery.
Kalinin is a Kaname/Sōsuke shipper. He's shown to hope that Sōsuke will "open his heart" and become more human if he ends up with her, and apparently started thinking of her as a hopeful daughter-in-law for his adopted son.
And then there's Melissa Mao, who, although less vocal about it, is a Tessa/Sōsuke shipper. In the novels, she even talks to Kaname, makes sure that Kaname is aware that Tessa is in love with him, and tells Kaname to be nice to Tessa. Mao proceeds to try to get Kaname to give an answer about whether or not she likes Sōsuke, and when Kaname gives a (rather ambiguous) answer that appears to be in the negative, Mao responds "that's good" and continues to show how she feels sorry for Tessa's passionate, but suppressed and unrequited love for Sōsuke.
In the real world, however, Takiko's maternal aunt ships Takiko with Dr. Oikawa.
In GaoGaiGar, every named kid except Ikumi Kaidou and the ship-ees are rooting for the Puppy Love ship of Amami Mamoru and Hatsuno Hana, who share a Childhood Marriage Promise. At the end of the series, before Mamoru and Galeon return to the Green World, the kids dress Hana in full tiny brides' regalia and stage a wedding, complete with kiss, to the wistful tune of "Someday in the Sea of Stars".
The Gundam franchise has plenty of these, believe it or not:
Hoy and Min, the grandkids of the man whose boat Domon is staying in, heartily ship Rain Mikamura and Domon Kasshu in G Gundam. Hoy even kicks Chibodee in the shins for trying to ask Rain out for lunch.
Gundam Wing: No matter what the Yaoi Fangirls say, practically everyone tries to get Heero and Relena to admit their feelings for each other. Late in the series Duo, Trowa, and Quatre encourage him to rescue her from White Fang (by himself) and discuss the relationship with surprising accuracy. In the manga Battlefield of Pacifists Duo and Dorothy make sure that the two meet for the first time in months and spend a good amount of time together. Hell, even Wing Zero (Particularly the suit's OS) seems to be pushing Heero in Relena's direction a couple of times.
Depending on whether one sees Trowa and Quatre as a couple or not, Heero, Duo, and possibly Relena could be seen as Shippers on Deck. Rather surprisingly, Heero is the most invested one, as he straight-up tells Quatre something by the lines of "don't you even think of getting yourself killed in battle before Trowa joins us again".
Roybea Roy, Shingo Mouri, Kid Salsamille, Jamil Neate and especially Toniya Marme from After War Gundam X ship Garrod/Tiffa. When Pala Sys joins the crew in the final arc, she immediately starts shipping it too. Truly, Everyone Can See It.
Miashei enjoys shipping her friends in Turn A Gundam. She's not hugely devoted to any one ship, but she'll happily comment on whatever looks likely at the moment (usually Loran with one of the Heim sisters, or Beta Couple Fran and Joseph).
Mileina Vashti in Gundam 00 ships Allelujah/Marie and Setsuna/Marina, desu!. And she actually is right about the first one (both if you include the movie's manga adaptation)!. Setsuna F. Seiei himself ships Saji Crossroad and Louise Halevy back together throughout season 2. He even slashed off Andrei Smirnov's Ahead when the latter attempted to kill Saji.
Gunslinger Girl: Triela is assigned to guard Mimi, a girl her age who notices her crush on her handler Hilshire and encourages her to let him know how she feels. Being well aware that Hilshire isn't interested in having an affair with a fourteen-year-old cyborg killing machine whose feelings of love are likely just a side-effect of her conditioned loyalty, Triela never follows her advice.
In fact, all the girls in their class seem to ship Mahiro/Nyarko; in the first episode, Tamao (falsely) told them that Mahiro said he could definitely see a relationship working, which caused all the girls (Nyarko included) to Squee!. Additionally, whenever Mahiro is particularly Tsundere, they encourage him to apologize and make it up to her. On the other hand, this might be because they believe the pair is already a couple, since Nyarko's class introduction involved claiming to be his wife (and people always seem to believe her lies).
Cuuko tries to ship Mahiro with Hasta in order to Pair the Spares; she wants Nyarko for herself. Hasta is totally fine with this, but Mahiro and Nyarko aren't.
The rest of the school also ships the pair to varying degrees. Most people, like Taniguchi, are just honestly under the impression that the two are already dating, while Kunikida brings up Kyon's supposed preference for "weird girls" whenever Haruhi does something strange.
Tsurya seems to think it's funny to push Kyon towards either Mikuru or Yuki, whoever he happens to be closest to at the moment. Then again, she thinks everything is funny.
Sirzechs ships Issei with Rias. He's very open about it too, putting ideas in Issei's head about using Boosted Gear Gift on Rias' breasts, and finding in very hard not to laugh when Issei starts raving at the top of his lungs about getting to have sex with Rias. For added hilarity, Rias happens to be Sirzechs' little sister.
Issei happens to be a shipper for Yuuto Kiba and Tsubaki Shinra because they look good together, and the fact that he wants Kiba off his back already. He's also this to Saji and Souna, but gets a bit harder to do when the latter insists that Issei calls her on a First-Name Basis.
Rin supports Sesshomaru and Kagura, becoming very excited when she thinks that Kagura might be in love with Sesshomaru, tries to convince Jaken that she's right, and says that they should trust Kagura more after she comes to this conclusion — seemingly trying to get them closer together. (ep. 167)
Not to mention Miroku, Sango and Shippo ship Inu-Yasha and Kagome pretty hard, and get angry at him whenever he seems to show feelings for his sorta dead ex... who also happens to be Kagome's previous incarnation.
Momo becomes one for Hibiya/Hiyori during Chapter 19 of the manga.
Ayano is the only person privy to Takane's feelings toward Haruka, and encourages her to confess her feelings when a particularly vicious attack from his condition has left him on life-support. She's too late.
Kaleido Star: Sora, Anna, Ken, Marion and Mia are Kalos/Sarah shippers. Their OTP becomes canon soon.
Sora also ships Jerry / Kate. Another one that goes canon.
Juugo Kannagi of Kaze no Stigma is very determined to see his daughter Ayano paired with once-family outcast Kazuma, going as far as to set up circumstances such as dates to amusement parks and hot spring resorts to try to bring them together.
Three notable ones in Kekkaishi. The first is Madoka, the best friend of the female lead, Tokine, who always overtly hints to Tokine that Yoshimori, the male lead and Tokine's childhood friend, would be a pretty good match for Tokine even though he's two years younger and Tokine has a preference for older, taller guys. The other two are Kyoko and Ayano, the two best friends of Yurina, a classmate of Yoshimori. They think Yurina's meetings with Yoshimori on the roof (which were actually discussions about Yurina's supernatural awareness) were attempts by Yuirna to confess to Yoshimori.
The Ryozanpakou masters in Kenichi: The Mightiest Disciple actively ship Kenichi with Miu, and even pay attention to any progress in their relationship...except for Miu's grandfather and the head of the dojo, HayatoFurinji, who's openly declared that the only way Kenichi will get to date Miu is by defeating him. Saiga Furinji, Miu's Disappeared Dad and the Big Bad, seems to approve of Kenichi's feelings for Miu, too; it helps that Kenichi was willing to go all-out to rescue her when she was kidnapped by Silcardo Junazard. On a lesser note, Freya has made the assumption that Kisara and Ukita are an item, though Kisara vehemently denies it.
Giroro's pet cat seems to know her owner has a serious crush on Natsumi, and seems to alternate between being jealous and resenting her for not reciprocating,or even noticing, Giroro's feelings.
Natsumi seems to be this for Fuyuki/Momoka. In one episode, Momoka called Fuyuki, causing Natsumi to have a mischievous look, nudge Fuyuki, and encourage him to go get her. However, Fuyuki, being Oblivious to Love, didn't get it. Aki seems to be one as well to a lesser extent.
In the manga Kyosuke's younger sister Manami ships Kyousuke/Madoka... while her twin Kurumi ships Hikaru/Kyousuke. Hilarity Ensues. It's played more seriously later, when Manami is the one who explains the whole Psychic Powers deal to Madoka because of this.
On the other hand, Madoka's Cool Big Sis-like friend Yukari ships Madoka/Kyousuke and leaves it clear in a scene where she playfully "links" them with a red string during a concert.
Karen of Kiniro Mosaic, in regards to Youko and Aya's relationship. In fact, in episode 5, she even made an "Ayaya Pie Chart" that consisted of 10% intelligent, 10% shy, and 80% Youko. Aya's reaction was priceless.
Shouko's younger sister Yuzuru doesn't hide the fact that she ships Shouko and Ishida.
A more subtle one is Kawai actively pushing Ishida and Ueno back together by arranging a get-together at a theme park. Which is disturbing when one remembers what Ueno, Kawai and their friends did to Shouko and later Ishida in elementary school and especially now that Ishida and Shouko are getting closer.
Kotoura-san's Haruka and Manabe is so clearly a couple that people in the universe just can't stop shipping them.
In episode 3, the boys in Haruka and Manabe's class put their names under an Umbrella of Togetherness signifying a relationship. Manabe at first seems offended by it, but rather than take offense that they shipped them together, he complains that they forgot to add hearts to it.
Haruka's grandfather (who is her remaining parent figure) is all for the couple, too; in episode 6 he is keen to see them kiss.
In (at least the animated adaptation of) Love, Chunibyo & Other Delusions, practically the entire class ships Yuuta and Rikka. This is especially noticeable at the start of episode 3, where the entire class gathers around and starts applauding at Yuuta's accidental Indirect Kiss. By episode 7, Nibutani makes it fairly clear that she believes Yuuta and Rikka are bound to be together eventually. Isshiki also takes a Yuuta/Rikka relationship as a given.
Most of this is brought over into the Macekred adaptation Robotech: Claudia and Vanessa often try to get Rick to realize his feelings for Lisa, as in the original, and Max still has front row to Rick and Lisa's kiss.
In the Magical Girl Lyrical Nanoha ViVid manga, half of the Numbers come to check out the sparring matches between Vivio and Einhart "because it's romantic." The other half just want to make sure nobody gets permanently hurt.
And of course Chamo ships every pairing that he's aware of, mostly because he gets oodles of cash every time he brokers a pactionote a magical contract where a mage gives a mundane partner power and possibly a powerful artifact in exchange for aid in battle, and since the pactios are typically made by kissing...
Shiho asks Mai to become one for her and Yuuichi in Episode 6, and Mai accepts. Unfortunately, when Yuuichi expresses his love for Mai with Shiho present in Episode 13, Shiho becomes very angry and accuses Mai of lying to her.
Suzu Sakuma in the Marmalade Boy manga, who, when Meiko says she is in love with someone that she can't be with, jumps a mile to the conclusion that this someone is obviously her best friend's boyfriend and Suzu's tutor, Yuu. She concludes that Meiko and Yuu would be the most beautiful couple ever and plots accordingly to break up Yuu and Miki. Made absolutely hilarious by the fact that a) Meiko is actually pining for her ex-teacher and b) her own cousin Satoshi is Yuu's best friend and absolutely nuts for Meiko. Love Dodecahedron? Oh yeah.
Note that in the original draft of the story, Meiko was supposed to end up with Yuu after Namura's death and, apparently, Miki getting hitched back with Ginta....
Miki starts shipping Meiko/Namura, then also becomes a Ginta/Arimi fan. Her boyfriend Yuu doesn't ship Meiko/Namura so openly, but the fact that he was their Secret Keeper should say something.
Tsutomu starts as Arimi's Dogged Nice Guy, but when she makes clear that she loves Ginta, he gives up and becomes their biggest fanboy.
Mamotte Shugogetten: Shaorin/Tasuke get shipped by Nana (his older sister) and Shoko (their classmate and Shao's best friend); in fact, Nana and Shoko have joined forces and are actively co-operating to get the two together.
In Mawaru-Penguindrum's episode 6, after Shouma Takakura takes the feverish Ringo Oginome home back home, Ringo's mother Eriko doesn't seem very convinced when Shouma says that he and Ringo are Just Friends... To be "fair", she just saw Ringo pretty much humping Shoma in a feverish pitch.
As of episode 11, it looks like Himari might ship Shoma/Ringo. She notices that Shoma cooks a special cabbage recipe only when he wants to make up with someone else, and then deduces he's worried for Ringo and says "I hope Ringo-chan likes cabbage!" Though this being Himari, she might be meaning this in more of a friendshippy take. Her "possessor", however... well, we don't know. She's a wild card.
Even more so: Yuri, the girlfriend of Ringo's crush Tabuki, also ships it. (Conveniently for her, but still). Yuri does ask Ringo if she loves him in that same episode and isn't convinced when Ringo denies it, claiming that she could see it coming from a mile away or something like that. Then it's subverted shockingly in episode 14 (when she drugs Ringo and tries to rape her because she looks like her sister Momoka aka Yuri's long-lost first love) and played kinda straighter in episode 15 (when, after Shoma fails to help Ringo and is knocked out, Yuri places him next to a sleeping Ringo, and when he recovers she teassingly asks him if he won't take advantage of her).)
Midori Days. In one chapter, Nao gives Ayase one of her father's "love potions". Ayase wonders why Nao did this, but passes it off as nothing. Later, we see Nao holding a notebook of a drawing with the three (four if you include Midori) together, holding hands.
Early in My Love Story!!, Takeo ships his best friend Suna with Rinko Yamato. However, it quickly becomes blindingly obvious that Yamato likes Takeo, who is Oblivious to Love after a lifetime of seeing girls prefer Suna. As a result, his shipping nearly blows the whole thing until Suna, who's fully aware of who likes who, plays shipper himself and gets Yamato to confess her feelings multiple times while Takeo is in earshot. After they're a couple, Rinko offers to hook up Suna with a friend and gets promptly shot down.
Oosaki Nana of Nana ships Hachi and Nobu and is angry and disappointed when Hachi gets pregrant and chooses Takumi.
Ino and Kakashi shipped Asuma/Kurenai before anyone else was wise to their relationship. In one scene, Ino knows the flowers Asuma wants are for Kurenai before he even tells her.
Naruto ships Shikamaru/Temari. He gave Shikamaru a big "good for you" grin and believed Shikamaru and Temari were on a date when they were seen walking together.
Neji also appears to ship Naruto and Hinata, suggesting that Hinata should see Naruto off at the end of Part I.
Sai told Sakura how Naruto feels about her, however he also subverts it by saying that Naruto's feelings for Sakura (and Sasuke) are causing Naruto nothing but pain.
Konohamaru and Gamakichi both imply they think Sakura is Naruto's girlfriend at two different points in Part I, even both using the same extended pinkie hand gesture that, in Japan, is used to signal "girlfriend".
In the flashbacks, Nagato (young Pain) was a Konan/Yahiko fanboy.
In a filler episode, Shino refers to Hinata's feelings for Naruto as the most crucial secret of the Allied Forces.
Kakashi appears to be quite the Sasuke/Sakura shipper, when in chapter 693, he speaks on behalf of Sakura and lectures Sasuke on how much Sakura loves him and how far she's willing to go for him.
In The Last: Naruto the Movie, Sakura clearly ships Naruto x Hinata, comforting Hinata and offering her the seat next to Naruto she was sitting in. It's thanks to her that Naruto has his definitive Love Epiphany regarding Hinata.
Akari pushes for Junpei/Kanako, although she doesn't mind Junpei/Mizuno too as long as she gets Kotone out of the Love Dodecahedron.
Mizuno, being still oblivious to her own feelings fr Junpei (along with an I Want My Beloved to Be Happy), seems quite supportive on Junpei/Kanako, to the point of believing that the two are already dating.
Tendou Akane from Ojojojo really wants Haru and Kawayanagi to get together and does whatever she can to get the two to interact with each other more. She continues this behavior even after the two of them get together.
In One Piece, several anime-only scenes have two conductors from the Water 7 train station ship Nami and Paulie together after seeing what appeared to be, to them, a breakup.
Both Kakeru and Uta, in Onegai My Melody, are Cannot Spit It Out types. Unsurprisingly various characters attempt to ship them — Flat the mouse, in particular, exists for no other purpose. And in Season 2, even Kakeru's romantic rival Jun Hiiragi can't help but plod him along.
Brianna, Soledad, Harley, and Drew's own Roselia are ContestShippers. Even Jessie seemed genuinely interested in the proceedings, talking about love and romance upon seeing them and weirding the hell out of James and Meowth.
Poor Ash Ketchum has been shipped with every female companion in the series by some Character of the Day or other. For instance, Lyra (the HeartGold/SouldSilver female lead) showed herself to be a Pearlshipper (Ash/Dawn).
In the Japanese version of Pokémon 2000, Jessie tells Misty and Melody that they're too young to worry about relationships, and James adds that "even we don't talk about such things". Meowth responds to Jessie and James by saying, "Whatever you say. You two act love-love all the time!" In the English dub, Meowth's line is changed to "Yous two don't need the opposite sex 'cuz you got each other!". He promptly gets yelled at for his trouble.
Dawn, May (and maybe Ash) appear to be LagomorphShippers (Pikachu/Buneary). Bonus points in that that's a perfectly legitimate pairing in the games.
In Best WishesStephan seems to be a SommelierShipper (Cilan/Burgundy) judging by his interaction with both of them and is obviously trying to get the two do stuff together (AKA the Sommelier battle). Burgundy didn't take this well and Cilanseems oblivious (or is he?).
Max, in the Japanese version, is a subtle Advanceshipper, since he mentions that he was happy in seeing his sister and Ash travelling together.
Miette in XY pretends to be a romantic rival to Serena for Ash's affections, but it's implied she's only doing it so Serena can get out of her Cannot Spit It Out stage.
Out-of-universe Amourshippers are also recently thrown a bone when Bonnie, who was so obsessed with trying to hook her brother up with any girl the group meets, has finally taken notice of the complicated Love Triangle that was Serena-Ash-Miette.
In Project ARMS, Yugo ships Ryo and Katsumi after realizing how much they love each other. Keith Green does too, though it's very brief since he dies not long after he decides this.
Sayaka plays it straighter in the manga, when she imagines Homura and Madoka embracing while calling it "the mystery of the universe"
In Rebellion, Homura somewhat makes her opinion known on that matter, in a rather twisted way. Twice. By creating an 'ideal world' inside her witch barrier, and later by rewriting reality. In both worlds she has Sayaka-Kamijou-Hitomi Love Triangle resolved by preserving Hitomi and Kyousuke's relationship, and apparently opts for Sayaka to be in a Romantic Two-Girl Friendship with Kyoko. Also, it seems like she's somewhat fascinated by the idea of Mami and Nagisa/Charlotte together.Hmmmm....
Queen's Blade: Hide & Seek has an incestuous example. In chapter 28, Leina reveals that she knows about her older sister, Claudette's, feelings for their younger sister, Elina. She not only tells Claudette that she shouldn't hide her feelings, but basically says she's okay with the idea of them being together.
Ukyō Kuonji tries to set up Akane/Ryōga a few times, since she's in love with Akane's fiancé Ranma. Unfortunately, since Ryōga is a combination of No Social Skills and horribly shy, it's usually a disaster. Shampoo also tries a cruder version of this by brainwashing Akane into falling in love with Ryōga, with equally disastrous results.
In the manga Ranma himself ships Ryōga and Akari, and so does Akane. Ranma and Akane even teamed up to ship them once.
OVA 10 has Ryoga and Ukyo attempting to break up Rakane, which ultimately backfires due to a misunderstanding that ends with Ranma and Akane shipping them.
In at least one episode of the anime, Mousse ships Ranma and Akane. Of course, he makes no secret of the fact that's because it should leave him with Shampoo by default.
Akane blatantly ships Kasumi and Dr. Tōfū once she gets over her own Precocious Crush on him, despite Kasumi's obliviousness to Dr. Tōfū's feelings.
And, of course the uber-examples, Sōun and Genma, who engaged Ranma and Akane in the first place and ship them at every opportunity thereafter. Kasumi, Nabiki, and Nodoka all have their moments of Ranma/Akane shipping as well. Dr. Tofu seems to ship Ranma/Akane right from the start, as well.
When Genma was going to make Ryoga his aire to the Saotome School of Anything Goes Martial Arts he along with Tendo, Kasumi, and Nabiki start to ship Ryoga and Akane.
Tybalt, of all people, ships Romeo/Juliet. Rather ironic when you consider his role in the original work...
Cordelia and Antonio are Rome/Juli shippers too.
Even Ciello, Romeo's flying horse, seems to ship Romeo/Juliet, considering all the times he's suddenly swooped down and landed in an apparently random, out of the way place so that they'll meet up, and that time he got them to ride him together.
Juliet is a Benvolio/Cordelia fangirl. She gets to see them get married, but doesn't live enough to meet their first child, of whom she would've surely been the godmother if she had survived.
She also ships Naru and Umino, mostly to help Naru out of her depression after Nephrite dies, and later for real once she sees the pairing more or less works. In an exception, she did not ship Naru with Nephrite himself, since she knew that he was working for the Dark Kingdom and thought he wasn't good for Naru; she was still sad when, in the end, he came to love her... and died.
Also, as soon as Rei understood that Mamoru and Usagi were destined to be together, she stepped aside immediately and urged Usagi to act on her feelings. This is given a small nod in Stars, where she also speaks to Usagi abut Seiya's feelings.
Weird variation. TenmaTsukamoto knows that KenjiHarima is deeply and desperately in love with a young girl whose name she doesn't know, and actively supports him in his pursue of her. Something else Tenma ignores is... that she is the girl Harima is crushing on.
The random old guy who shows up to give Hinai mysterious advice (no, he's not an Old Master, he's just some guy) ships Mikoto with Hinai or Aso, depending on who's closest at the moment.
Old Guy: He's off his guard! If you want to score, now's your chance, you sexy little squirrel! Mikoto: Say what!?
Keiji is an enthusiastic supporter of Kenshin/Kasuga, despite Kasuga's embarrassed protests.
On the opposite side, Yukimura seems to ship Sasuke/Kasuga, again despite her protests.
Kaoru of Servant × Service supports Lucy/Yutaka, to the point that she sets up a gambit to make her brother's one-sided crush on Lucy a mutual one.
7 Seeds: Fujiko and Chisa become shippers for Hana and Aramaki during the Mountain/Ocean arc, trying to get those two to be together (alone) as much as possible, despite Hana being in a relationship, Aramaki knowing this and finding her boyfriend is one of Hana's big goals in the story.
Yashiro does his best to get Ren together with Kyouko and even goes to far as to attempt forcing Ren to admit that he loves Kyouko and telling Kyouko bluntly that Ren loves her — Ren gets annoyed with this behavior, while Kyouko completely ignores it.
On another ship, Shoko in later chapters serves as the opposing Shipper On Deck, as a Sho/Kyouko fangirl. She, at first, doesn't believe that they are not dating. Later, she tries to make Sho admit that he has feelings toward Kyouko, going so far as to — in the Valentine's arc — take him to visit Kyouko at work on Valentine's Day to "win her back". He proceeds to steal her First Kiss in front of Ren (and Yashiro) but turns the situation into a declaration of war on Ren rather than a proclamation of love for Kyouko
In Slayers NEXT, Amelia reveals herself as a Lina/Gourry fangirl after Lina fakes her death to kill the demon Mazenda and recover her powers (which Mazenda has sealed away), which prompts Gourry to call her insensitive and ask "don't you know how I feel about you?" Amelia perks up at this, claims she saw this coming from a mile ago. and drags a bemused Zelgadis away, insisting that they give a now embarrassed Lina and still clueless Gourry some privacy.
In the third arc of Spice and Wolf, pretty much everyone except Amati ships Lawrence with Holo. Mark and his apprentice go to lengths to support Lawrence's scheme to win her back, despite only seeing them together once, and Dianna thinks up a secret plan to reaffirm their trust in each other. Batos also helps Lawrence out, but that's arguably just because he's taken a liking to him.
Magma from Spider Riders seems to be a Hunter/Corona shipper. While the hero Quake/Brade seems to think Hunter/Aqune would be just as good as a pairing.
Ryou, the lesbian Visual Kei idol from Strawberry Shake Sweet. Her Gaydar is so powerful, she can literally see the sexual tension between the protagonists Julia and Ran; and though it's never explicitly stated, her actions in certain episodes make it plainly obvious that she's trying to get the two girls together.
Matsuri Hojou from Sukisho appears to ship Sora and Sunao together to the point where he forces them to participate in a clue hunting game alone together to get them to reconcile
Justified Trope in the Robotech continuity: Dana's the result of a similar relationship (a human Veritech ace and the female Zentraedi who micronized herself and snuck aboard to kill him for beating her in battle but fell in love with him), so she can understand Bowie's plea better than anyone else.
In Switch (2002), Hiki encourages Mari's affection for Kai and tries to create opportunities for her to confess to him.
Almost all of the cast in Tengen Toppa Gurren Lagann ship Simon and Nia, and early on a number of them were Kamina/Yoko shippers, too. Leeron is an outright shipping fanboy.
Maria attempts to do this for Mio and Basara in The Testament of Sister New Devil. It's a rather interesting combination, as she's a succubus, Mio is the daughter of the former demon king, and Basara is descended from the hero tribe, a group that fights demons.
Adale in The Good Witch of the West, who gleefully writes what amounts to in-universe Yaoi fanfics that unsubtly pair off both of the female lead's male suitors with each other. It is implied that the reason she fantasizes about this is so she can claim the heroine for herself, although nothing comes of it.
In The Prince of Tennis Momo, Inui and Eiji are Ryoma/Sakuno shippers. In the anime, so is Ryoma's father Nanjiroh.
In last manga chapter/OAV: Inui comments on how naive Tezuka is as he hears the other tell Fuji to not speak about how he *can* smile, and this makes Inui look like a Tezuka/Fuji fanboy.
In The Wallflower, Noi becomes a Kyohei/Sunako shipper early on, regularly fangirling about their "moments" together. The rest of the major characters eventually follow suit, trying their damnedest best to get Kyohei to realize his feelings for Sunako as the Belligerent Sexual Tension between the two of them becomes increasingly clear in later volumes.
Maho from Wandering Son initially supported her sibling Nitori and her best friend Anna being together however her opinions changed later. She had a negative view on ther relationship due to Nitori's femininity, however eventually she mellowed down about it.
Played for comedy in Tokyo Ghoul:Re. After learning about Miza's crush on his gang leader, Shousei pledges his full support to her efforts. He later spies on her disastrous attempts at flirting, while wearing a "SUPPORT" headband and hoping to witness "child-making" between the couple. Too bad for everyone that Naki is Oblivious to Love.
Momo's trying to create a harem for Rito, after all. She appears to be considering each and every female except Peke and his Mom as a love interest.
Lala also fully supports Rito/Haruna, with the added twist that she is hoping that it'll lead to Rito/Haruna/Lala.
Risa (and her best friend Mio) seems to be pushing for the Rito/Lala ship, and has been nothing but helpful to Lala in trying to get them together, albeit in her own way.
Nana is the edge of this when it comes to Rito/Lala and Rito/Haruna.
Mikan appears to want Rito/Lala, considering she keeps chastising Momo for coming on to Rito, saying that it'll make Lala upset. However, this could also be due to her own jealousy.
Yuu wants Rito/Yui, although he is sympathetic to Rito's trouble-filled life.
Saruyama has often helped to encourage the Rito/Haruna ship.
Oshizu supports Rito/Haruna. Using her ghost powers. Usually ends in FanService.
Saki supports Rito/Yui and sets up a date between them in chapter 52.
Toradora! has pretty much every character as a Shipper on Deck, Combined rather painfully with I Want My Beloved to Be Happy. At first, Taiga and Ryuuji do this for each other (with Ryuuji/Minori and Taiga/Yuusaku respectively). Meanwhile, every other character not genetically related to Taiga ends up at some point shipping Ryuuji/Taiga.
Ishtar from Vampire Game. By far the best pairing she comes up with is Illsaid and Duzell, especially because she pretends Duzell is her little sister to pull it off.
With the Light features this in a one-off scene: after one mother comments on how happy her son was when Hikaru (an autistic child) brushed against his cheek, another mother grinned knowingly as she pulled out a drawing pad and pencil...
Everyone in ×××HOLiC seems to ship Doumeki/Watanuki, with Watanuki's employer, Yuuko, being the biggest shipper of all. Others include Yuuko's fortuneteller colleague, and Himawari, the girl Watanuki has a crush on. Even young Kohane picks up on that Doumeki and Watanuki are good friends despite any protests.
It gets to the point where Watanuki starts claiming that the entire female camp is against him.
Watanuki: Why do all the women misunderstand!? *sobs*
Not just all females: Mokona ships Doumeki/Watanuki too. He's shown to constantly try to hint to Watanuki that Doumeki likes him — including chiding Watanuki for berating Doumeki, as Doumeki is trying to spend time with Watanuki because he wants to "make sure Watanuki isn't hurt... in heart, or in body."
Though, after Watanuki pulled his I Will Wait for You stunt for Yuuko upon her disappearance, Haruka seems to have reluctantly begun to accept (and ship?!) Yuuko/Watanuki, literally giving Watanuki a heart-to-heart If You Ever Do Anything to Hurt Her... talk. Wonder how Doumeki would feel if he knew that he was betrayed by his old man.
Nakajima's parents might count, especially his stepmother. It helps that both of them are fond of Miyuki.
There is a scene in the Yu-Gi-Oh! manga where Mai Kujaku is seen actively setting up Yuugi Mutou and Anzu Mazaki. Later, just before Battle City starts up Mai pointedly teases Anzu when it looks like she's on a date with Yuugi. It's not really, but it's the thought that counts.
Can't speak for the manga, but Atemu in the anime is very supportive of Yuugi/Anzu. He's teased and prodded Yuugi about his crush on Anzu on multiple occasions, and he was quite disappointed in episode 53 when he realized that he was the one meant to go on the date with Anzu, not Yuugi.
According to some fans, Anzu might be a Jounochi/Mai shipper, getting angry at Jou more than once when he blows chances at wooing her.