Zone of the Enders: The Fist Of Mars has the entirety of BIS shipping Cage/Myona at one point, and towards the end, Yukito ships Warren/Mebius. To be fair on the latter one Everyone Can See It, and Warren DOES have a crush on her
Cecil: "Say, why did you desire to protect Terra?" OK: "Huh? It's because—She's been uneasy since we met, so I thought I needed to protect her." Cecil: "So you've fallen for her, I see." OK: "Tha-that's not the reason!"
In Fire Emblem: Radiant Dawn, Micaiah refers to the "warm feelings" Naesala has for Leanne, and that Soren has for Ike. Additionally, Ike was astonished to discover that Jill and Haar were not cohabiting.
In Fire Emblem: The Sacred Stones, Moulder is the first one to notice that Vanessa has a Bodyguard Crush on their lord of liege, Prince Innes. He tells her stories about Innes's childhood and encourages her to tell him what she feels. Ironically, due to the nature of the Support system, pursuing Moulder's line makes it impossible for Vanessa to hook up with Innes in that playthrough... Meeeep.
Vanessa's older sister Syrene also encourages Vanessa's feelings, but it's not clear who does she ship her with. The guy's name isn't mentioned so it could be either Innes or her other possible husband, Forde.
Vanessa and Syrene's friend and co-worker, Gilliam, has strong feelings for Syrene but doesn't mention them since he's The Quiet One. If you make him strike a friendship with Garcia, in their last support Garcia will encourage Gilliam to be open with his love for her when the war ends, and finishes saying that he should invite him and his son Ross to his wedding. (Again, the nature of the Support system will "cockblock" Gilliam from openly talking to Syrene in that playthrough.)
Another, even odder example is Lucina, who accuses a female Avatar of trying to seduce her father if the latter is not already married to him. When the Avatar denies this, Lucina launches into a tirade about her father's "wonderful charms" and basically demands that the Avatar fall for him. And all of this only happens if Chrom (and possibly the Avatar) married someone else, meaning that Lucina is defending a ship that sailed before she was born. Time travel can be weird like that.
Throughout Kingdom Hearts II, Donald Duck and Goofy supportively tease Sora about his feelings for Kairi. When Kairi and Sora reunite in the end and share a tender embrace, the camera cuts to Donald and Goofy looking pleased.
Sora can act like this for the canon Disney couples. He gets downright misty-eyed when Mulan and Shang are appointed the Emperor's joint bodyguards, and seems to approve of Will and Elizabeth (which leads to some of the aforementioned teasing from Donald and Goofy).
In a somewhat weirder incident in Days, Xigbar gives Roxas dating advice for impressing Xion. The catch, of course, is that this relationship fast turns into one huge Shapeshifting Squick, and Roxas hasn't a clue. Given that Xigbar knew this, he was probably just being a dick.
And let's not forget about Olette. When Kairi stumbles into Twilight Town, befriends the gang, and tells her story about Sora and the others (i.e. the events of the first Kingdom Hearts), Olette is utterly mystified by it, going as far to call it "romantic."
In Chain of Memories, Tidus, Wakka and Selphie tease Sora about his feelings for Namine, and Selphie says, "Go get her, cowboy." This whole scene is a lie that the Organization forced Namine to construct.
In fact, pretty much the entire party seems to be supporting Colette's crush upon the clueless Lloyd... Except for Zelos, who seems just as intent on cluing Lloyd in on Sheena's crush on him... If only because he knows it aggravates the latter.
Norma in Tales of Legendia can't help but give advice to Chloe for attracting Senel's attention. None of it works, mind you. To add to the weirdness, she also helps Shirely with her relationship with Senel. Norma just likes to mess around with relationship for the fun of it, it seems.
Subverted in The Legend of Zelda: Ocarina of Time. After the player wins the Cucco-hunting minigame, Talon raises the suggestion that Link marry his daughter Malon. Whether Link says yes or no, he swiftly laughs it off as a joke, however.
Also in the Zeldaverse, it's implied that most of the residents of Ordon Village ship Link/Ilia in The Legend of Zelda: Twilight Princess. This seems to be largely due to her status as the mayor's daughter and their hopes that he'll be mayor one day, plus the fact that they're good friends and close in age.
Given the true nature of that world, and of Welch, it may be an attempt by a fan to run the asylum.
Apparently in Samurai Warriors 3, Kaihime and Keiji encourage Kunoichi to confess to Yukimura, while Magoichi also comments that Yukimura is a lucky dog for having Kunoichi by his side, while Kunoichi herself is more of a Yukimura/Inahime shipper in Inahime's musou mode.
In Persona 4, Rise ships Kanji/Naoto. The main character also has the option to approve of this pairing. She also ships Yosuke/Chie, which creates a hilarious he's not my boyfriend moment. It should be noticed that Rise also ships herself with the protagonist, very overtly; it's possible she both tries to weed out competition and thinks the other pairings are cute.
Just about everyone shipping Squinoa in Final Fantasy VIII. Especially Selphie. Concert anyone?
Mere peanuts compared to the shipping child!Ellone did for Laguna / Raine.
Auron seems to ship Tidus and Yuna in Final Fantasy X, repeatedly making comments to Tidus to guard Yuna, stay by her side, don't push her away, etc. Rikku also seems to approve.
Whereas some of the others try to drive them apart, not so much because they want one or the other for themselves, but Yuna was going to die until they said Screw Destiny.
If you try to express interest in Mira as a male character in Knights of the Old Republic 2, she points out rather bluntly that Visas and the Handmaiden are both infatuated with you and she doesn't want to have to beat them both off if she starts sharing a bunk with you. To the dismay of many fans.
This is because fans were disappointed about this not being an option in the first game (after all, you can romance Liara and she's an alien). So the developers wanted to make sure their fans didn't overlook the option in this game expecting it to be like the first.
And one of the DLC squadmates, Kasumi Goto, is in on it too, and will comment on all of your relationships. For example:
Kasumi: Tali is so cute. You're all she ever talks about, in that sweet "rainbows and butterflies" kind of way! She loves you, Shepard. Be good to her.
According to Kasumi, most of the crew are shippers when it comes to Fem!Shep/Garrus, commenting "A lot of people want to see you together." when you romance him. This is also a Lampshade on their wild popularity in the fandom.
There's an advertisement on the Citadel that ships Shepard with... whichever potential love interest (if any) is in your party when you click on it. ("The next time you're out on the town with [Officer Vakarian/Sere Krios/Mr. Taylor/Miss Zorah/Miss Lawson/ERROR: CITIZEN ID NOT FOUNDnote (Jack, in case you were wondering)...") It'll even mention Justicar Samara, who isn't actually fully romanceable. Alternately, if you're in a relationship with one of the ME1 squadmates and there's nobody romanceable in your current party, it'll mention that love interest instead.
In Mass Effect 3, Shepard can become a Joker/EDI shipper, pushing the former to "go for it" and giving the latter dating advice.
Also in 3, assuming you talked Liara into talking with her "father" Matriarch Aethyta, at one point in their conversations Aethyta will ship Liara with Shepard.
Tali, however, ships Liara and Javik, assuming you've downloaded him. There's a bit of dialog from a hung over Javik in the Citadel DLC to suggest he might go for it.
Even funnier in hindsight, since Isaac and Jenna did get together, at least long enough to produce Matthew...
The lesser-known happens if you trigger Feizhi's brief cameo at Champa, in which she's searching for Isaac to give him a little thank you gift, a Golden Ring. Kraden openly encourages her to pursue the matter further, much to Feizhi's dismay.
Kraden might be at it again in Dark Dawn, since his excuse for Nowell's absence in the second half of the game is that she took a fancy to Piers, which he may or may not have encouraged.
Many people who originally tried to hook Akira up with Mika suddenly switch to Akira trying to get along with Atsuki. Akira's father of all people has a more noticeable switch in the last chapter of the game when he mentions that all his son talks about is Atsuki and how if Atsuki plans on leaving, he should come back because he's welcome. Note that this is what he said to Mika earlier in the game and while it still applies he's referring to the fact that Mika is like the daughter he never had.
Then there's Nami who despite shipping herself with Atsuki, has dropped a lot of hints concerning why Atsuki constantly chooses Sweet Ring (the restaurant Akira's father owns and where Akira works) to eat out whenever he takes his friends out. Shortly after she says that, Akira shows up and her sprite has this funny smile on her face.
A minor character Shunichi in episode 19, stops searching for his friend to talk to Atsuki. While the original conversation was about his friend Kyosuke having a girlfriend (which he assumes is Mika), he suddenly asks about Atsuki's preference. The correct answer is saying that Atsuki isn't interested in dating (girls) and Shunichi suddenly assumes that Atsuki likes Akira (and the player is assuming that Atsuki denies it with how quickly the conversation changes).
King/Ryo Sakazaki: Ryo's younger sister Yuri, father Takuma and best friend Robert Garcia are very blatant in their support (to very silly and awkward degrees in XI). Takuma's own share of support might be going to the "I Want Grandkids" extreme; it makes sense since Ryo is the eldest son, the Heir to the Dojoand already in his mid 20s (Comic Book Time be damned). Oddly, Takuma goes the OPPOSITE way in regards to Yuri and Robert because he feels the playboy Robert might take advantage of his baby girl... despite Ryo actually supporting his little sister's feelings for Robert in Art of Fighting 3.
Sie Kensou/Athena Asamiya: The earliest shipper is the aforementioned Robert, since his 2001 win quote against Kensou has him say, "Hey, let me know what's up with you and that girl!" By XIII Yuri, King, Mai Shiranui and Joe Higashi have eagerly joined in, mentioning Athena and teasing Kensou about her in either their pre-fight talks (Yuri, King, Joe) or their winning quotes (Mai).
Robert Garcia/Yuri Sakazaki: Mai Shiranui, and most likely King as well. In Mai and Robert's XIII pre-fight talks, once Robert ticks her off via pointing out hiw Stripperiffic her outfit it, Mai openly refers to Robert as "Yuri's boyfriend" in the middle of a Rant Inducing Slight. It's specially notorious since Yuri and Robert's potential romantic relationship has been downplayed in the KOF continuity.
"Sorry Yuri, but I'm going to take your boyfriend to the trash!"
Kyo Kusanagi/Yuki: In the KOF:KYO semi-canon continuity, Athena and Kensou seem to support their relationship once they get into Kyo's circle of friends. (Though it may be an "I Want My Belovedto Be Happy" from Athena.) Kyo's sort-of pupil Shingo Yabuki also is pretty partial to it, and so are Kyo's Happily Married parents Saisyu and Shizuka. Chizuru is Genre Savvy enough to actually exploit Kyo and Yuki's bonds in the game, asking Yuki to lay low and using her sudden absence as a Secret Test of Character.
Various party members will eventually become this for the Warden and his/her chosen Love Interest in Dragon Age: Origins. Wynne, in particular, initially expresses misgivings but in time changes her mind in support of the relationship. Morrigan, if her approval rating is high enough, may engage the Warden in a playful discussion about the matter; it's especially moving and also touching if the Warden is female and romancing Alistair - whom Morrigan otherwise loathes.
In Dragon Age II, Merrill actively ships Hawke with any of their chosen Love Interests, Isabela threatens a Hawke romancing Merrill with grievous harm if they hurt her (if female) or cutting their balls off (if male). She also apparently writes erotic "Friend-fiction" in her spare time; Varric finds it hilarious.
Snarky!Hawke jokingly ships Meredith and Orsino and calls them out on their Foe Yay.
Snarky!Hawke: Honestly, the way you two go on. People will talk!
Played straight in regards to Jin/Tsubaki. Both Noel and Makoto think the two make a nice couple - Makoto in particular teases Tsubaki about this ship whenever the opportunity arises. Case in point:
Makoto: Oh, hey, congrats on being assigned to the 4th Thaumaturgist, yeah? Ministerial Secretary to mister Jin Kisaragi himself! Man, what I wouldn't do for your brains! Tsubaki: It was dumb luck, I swear. There was an opening, I hadn't been placed yet, end of story. And it's not even official yet. Makoto (with trollface): Tsubaki, this is me you're talking to! Drop the good little cadet shtick and just say it! "I'm gonna spend every day with Jin, and I couldn't be happier about it! Tra, la la, la la!" Tsubaki: I... what? Huh? What makes you think I'd say that? Makoto: Somebody's blushing~! *giggle* Geez, I can read you like a book when it comes to that boy. Tsubaki: Well, you... need... reading glasses, I suppose!