It's implied that Tom Nook and Sable were in love in their youth, however when Tom came back from the city a more cynical and money focused individual their romance died. Fans are quick to get them together in fan material.
Despite the series lacking much romance, many New Leaf fanworks portray the protagonist's assistant Isabelle as harboring a crush on them.
For some reason, Hiroshi/Takuro is fairly popular in Ao Oni.
Ditto for there being far more Shaun Hastings/Desmond Miles out there than the canon-suggested Desmond/Lucy.
The most popular Assassin's Creed III ship is Connor/Aveline, despite (or perhaps because of) the fact that Connor has no love interests in his game and Aveline doesn't even appear in it unless you connect her PS Vita game to the PS3 version. Reams of fan art existed even before the games' release.
Ahriman's Prophecy's canon is Devin/Alicia, but he is more popularly paired with Talia, his Childhood Friend whom he shares better chemistry with.
In Aveyond 1, most fans think Lars/Rhen is a better pairing than the canon Dameon/Rhen. Dameon successfully flirts with Rhen in the game, but there never seems to be a spark, even when they get gushy. Then it turns out that Dameon is The Mole (though already revealed to the players around the beginning of the game), making even less of a reason for that pairing. And then we have Lars, who was once cruel to Rhen since she was Made a Slave to his family, then finds out she's royalty, and he apologizes to her rather awkwardly. Though it is rather obvious the game tries to enforce the Dameon/Rhen pairing and tries to avoid Lars/Rhen, it is even more blaringly obvious that the Lars/Rhen pairing is far more popular in fandom. Build C of the game throws Lars/Rhen shippers a bone by adding an option to have Rhen go back to Shadwood Academy with Lars, only to state in the epilogue that Rhen did marry Lars... or did she?
Talia/Devin from Ahriman's Prophecy also seems rather popular. Like the Aveyond 3 example, you can put them together in individual game play, but the canon pairing is Devin/Alicia.
The Japanese Bahamut Lagoon fandom ships Byuu and Frederica despite there being little evidence, and Byuu and Yoyo, who broke up in-game.
Baldur's Gate: Despite the creators attempting numerous times to invoke Abandon Shipping, male CHARNAME and Imoen have always and probably will always be the preferred pairing for a male character.
It's pretty known that Litchi is a Love Martyr for Arakune, but it doesn't stop people for pairing her with Bang. This gets even more prevalent when due to story development, Litchi's love for Arakune was one of the reasons why she pulled a Face–Heel Turn, thus if Arakune was not her main love, she would've no need for that. And surprise, Bang is revealed to possess a Nox Nyctores that might be the key to cure BOTH Litchi and Arakune and possibly annulling her Face–Heel Turn...
Jin/Noel has a rather healthy fanbase.
More recently, Kagura/Makoto has been gaining some traction, based on their interactions in Chronophantasma's Story Mode (namely mentions of an implied history between the two, and the fact that they get along and respect one another in spite of their squabbling).
Bloodborne: Despite the game involving absolutely no romance whatsoever, quite a number of fans pair up the Hunter with the Plain Doll, mostly due to the Doll's dialogue and her devotion to the Hunter as well as how the player can choose to (sort of) reciprocate her feelings by giving her the Small Hair Ornament, a key item that can only be found in a hidden location that requires some effort to reach.
In Breath of Fire Ryu and Rinpoo/Katt in II is a popular Fan-Preferred Couple in both the US and Japan, even gaining its own Portmanteau Couple Name in English-speaking countries. Scias x Ursula in IV is a fairly well-established Fan-Preferred Couple that has taken on a fanon life of its own. Ryu/Lin in Dragon Quarter is a similar case of a Fan-Preferred Couplenote considering the Nina in that game is all of twelve years old and Ryu has more of a Big Brother Instinct towards her.
Dark Souls has Artorias the Abysswalker paired up with Lord's Blade Ciaran. Ciaran is the only character besides Artorias's wolf Sif who openly mourns him after his death; she's encountered kneeling at his grave after you kill him and will ask you to hand over his soul and equipment to her; and if you fight and kill her, Ciaran's last words (unsubtitled) are actually, "My Dear Artorias". Hawkeye Gough even outright tells the player that Ciaran has feelings for Artorias, though it's unknown if Artorias reciprocated. The fandom tends to assume he did.
There's also a lot of support for Maiden Astraea and her knight Garl Vinland, which is pretty much canon anyway. Their tragic backstory and the fact that one will commit suicide if the other is killed only make the two even more sympathetic.
While there is no Official Couple in the game, the protagonist is capable of hitting on many of the girls, and thus many of them like him (which can really be said for everyone). However it's easy to see without the FATE route that Yamato develops as a person by just being in the protagonist's presence, originally seeing him as a pawn he can use, to seeing him as a capable leader, and then finally acknowledging the hero as his only friend that he can rely on. So if you take a route that isn't Yamato... he willnot take itwell at all. Given his backstory, though, it's understandable why he becomes clingy to the hero in the first place. The anime also doesn't help with upping Yamato's obsessive nature toward Hibiki and all the artwork promotes him, Hibiki, and Alcor (particularly one line where he tells Io that Hibiki is his, contrast to the game where he threatens to slash everyone's throat for daring to corrupt his hero).
The latter are popular more so in the anime than in the game. In the game, the two are partners but get separated because of Rolando attacking the Nagoya branch. Airi gets really angry if Jungo is killed and is relieved if he survives (mind you Jungo is one of the hardest people to save in the game). Jungo doesn't mind Airi using him as a way to vent her frustration and he always tries to cheer her up. Neither of them take it well in the game when they take different sides of the issue (she chooses law and Jungo goes neutral) when they fight each other in battle but are quick to forgive each other. In the anime Jungo is always saving Airi when she's in danger. Jungo puts Airi over everyone else in the party given his personality to save his friends. It makes their death painfully tragic because Jungo could have avoided his Death Clip but he chose to save Airi... but it ended up being in vain and Jungo realizes that when he stops running and holds her tightly before they're both blown up.
Before the sixth Dynasty Warriors game, Sun Shang Xiang was usually paired with any of the "hot" Wu guys like Gan Ning, Lu Xun, Ling Tong, or Zhou Yu as opposed to her canon Love Interest Liu Bei. Koei seemed to counter this by making Liu Bei much younger and attractive looking in DW6. Before he looked a good 15-20 years older than her. After doing this there was a noted rise of Liu Bei/Sun Shang Xiang fan art and fanfics. Mission Accomplished.
Guan Ping and Xing Cai. Despite her being based on the historical wives of Liu Shan, Koei has teased that they might have feelings for each other.
On the yaoi side of fandom, Ma Chao & Zhao Yun have had a strong fan following for many years (arguably an example of a Token Minority Couple, given they were both young, handsome, almost exclusively pre-occupied with things like honor and justice, and up until DW6, spear-wielders) before Koei decided to make it official and actually give them an in-game friendship. With proper cutscenes! And special dialogue!!!! Whether it was Koei taking notes or just pairing up the spares is anyone's guess.
Dota 2 isn't exactly one to attract coupling and such, but the fanbase also has several popular ships often based on gameplay synergy, resemblances, or in-game lines.
Sven/Crystal Maiden are very popular as the two are a popular and compatible lane-partner pair as CM's Arcane Aura alleviates Sven's small mana pool and her stun, Frostbite, is great in combination with the melee Sven's own stun, Storm Hammer.
Phantom Assassin / Omniknight are incredibly popular as they are also excellent in-game partners because Omniknight's Repel (which grants immunity to magic damage and disables) is invaluable on PA, who is incredibly vulnerable to them.
Death Prophet / Faceless Void gained traction during the height of the two's competitive usage. This is because of FV's Ultimate, Chronosphere, which freezes all units inside it, but FV. When combined with DP's ult Exorcism (which summons swarms of ghosts around her to attack enemies), whole teams can be devastated.
Slark / Naga Siren are the most popular example of a pairing based on in-game lines. Although the two do not reference each other in their backstories, Slark has one particular line towards Naga that gave a lot of fans ideas.
Slark (when greeting Naga Siren): Don't listen to the critics, Naga. I love your voice.
Similar to Slark and Naga are Wraith King and Queen of Pain. Asides the obvious "King and Queen" theme, several of Wraith King's lines indicate he has a strong lust towards Queen of Pain.
In The Elder Scrolls V: Skyrim, the Dragonborn and Serana from Dawnguard have been heavily shipped by the fandom, who praise her well developed character and how much depth was given to her burgeoning relationship with the Dragonborn. Many were disappointed that she's not a romance option, as despite the ship-tease, she politely turns down your proposal, stating her dislike of temples.
On the male character side, many players were bitterly disappointed to discover Brynjolf was not marriageable, as his friendly Loveable Rogue demeanor and affectionate use of "lad/lass" toward the Dragonborn throughout the Thieves Guild questline can come across as a little flirtatious. Worse, not only is he not marriageable, after you finish the Thieves Guild questline, he has no more than a single line of dialogue to spare the player anymore.
11eyes has Kakeru/Misuzu, Kakeru/Shiori and Takahisa/Yukiko.
Fans of Eternal Sonata think that Chopin and Polka have better chemistry than the Official Couple... despite the fact A) she's analogous to his real-life dead little sister, and B) he's twenty-five years older. A lot of this depends on what version you're playing, though.
For a time in the Mystery of the Emblem fandom, people greatly preferred Marth with Catria instead of his canon girlfriend and eventual wife Caeda/Shiida, whom they preferred to pair with Ogma. In an aversion of Die for Our Ship, they get along with Marth/Caeda fans, though.
For Binding Blade, since only Roy gets paired endings, a number of pairings that had material to be canon don't end up so, and thus became this among fans. Stand-outs are Rutgter/Clarine, Raigh/Sophia, and Noah/Fir. Roy's most popular choice of wife is additionally Lilina, which is a hair away from being canon.
For Blazing Sword, a surprisingly popular pairing amongst the steamy fan art crowd is Dark ActionMom Sonia Reed and her Number Two, Ursula the Blue Crow. It's not hard to see why: Ursula's Undying Loyalty to Sonia combined with Sonia's Alpha Bitch personality and penchant for wearing Stripperiffic black leather lead to obvious dominant/submissive implications, and they definitely seem closer than Sonia and her canonical husband Brendan (part of this may also be due to the fact that Brendan is huge, muscular, hairy, and in his fifties, making him an unlikely choice for steamy fan art).
The Tellius sector has a large faction of fans who still wish Ike and Elincia had gotten married instead of Elincia marrying her loyal knight Geoffrey and Ike leaving the continent either alone or with Soren or Ranulf. From the 10th game, pairing Micaiah with Pelleas is preferred to the canon Sothe/Micaiah.
Fire Emblem Awakening, due to the massive amount of marriage potential, generally doesn't apply but there are some exceptions, mainly Basilio/Flavia and Maribelle/Lissa, both of whom have a very solid relationship in their Supports and in story scenes.
Serah and Noel from the sequel got a lot of supporters MONTHS before the game was even out, with some hoping that Snow and Serah had broken up because he wasn't seen in earlier trailers. And then it got even more support after the game was released and contained some very Heartwarming Moments between the two.
Let's not forget the humble, but growing number of Warrior of Light/Cosmos shippers out there.
It doesn't hurt that, WoL's strong and undying sense of duty to his goddess aside, it is eventually revealed that the pair are actually perfect manikins respectively modeled after Cid of the Lufaine and his wife.
Despite the fandom's notorious shipping wars for every other character in the series, Saturos and Menardi are near-universally seen as a Battle Couple, despite there being no canon evidence of romance between them.
Felix's most popular pairing is with Sheba due to his Always Save the Girl moment for her in the first game, which is given a nod in Dark Dawn's recap of the story. Notably, they are the only two party members whose romantic fates remain entirely unknown, letting the shippers still hope that they could be canon.
The Harvest Moon fandom is almost entirely dedicated to shipping due to the series having a marriage system. However, it has become increasingly common for one or two bachelors to appear in most fanworks as the female main characters love interest (and it's almost always bachelor/female-protagonist due to the Cast Full of Pretty Boys in post-IOH games combined with the mostly female fanbase):
Marlin/Pony is the most popular ship for the main character in Harvest Moon Another Wonderful Life. This however is less due to Marlin being well-liked (though he has his fans) and more because he is the more tolerable bachelor, with Rock being seen as dumb and annoying while Gustafa is seen as unattractive.
Ib: Almost all the fics on AO3 with a romance aspect ship Ib/Garry. There is no Official Couple for Ib, probably because the main character is nine years old and Garry, her preferred love interest, is anywhere from eighteen to twenty, but that hasn't stopped the fans.
Inazuma Eleven has Endou and Aki apposed to the Official Couple Endou and Natsumi or Fuyuka depending on adaption though most of the fans got over it when they realized that she probably ended up with Ichinose.
Jade Empire has a maximum of three romantic options within the party... so, naturally, the most popular pairing is the PC/Sagacious Zu, a character who makes a Heroic Sacrifice right when the canon romances begin to play themselves out.
Kairi is semi-officially paired with Sora (they both are shown to like the idea of sharing a Paopu fruit with each other, which is pretty much a mythical engagement-ring). Among many fangirls, however, the pairing of Sora with his best friendand rival Riku is vastly more popular. There are also many who take a third option and ship them together in an OT3.
Also from BBS (more so among fans of yaoi), Ventus/Vanitas. This becomes Squicky because Ventus and Vanitas are technically the same person. However, as other pairings demonstrate, the semi-canon Xion/Roxas included, in the universe of Kingdom HeartsScrew Yourself isn't uncommon.
In Lamento - beyond the void there is a very sensitive war going on until today about who is Konoe's best choice for partner. Considering he have three options, it's not an easy discussion but Rai seems to be the favorite of the majority (and his ending is the so called "true ending" of the game).
Left 4 Dead 2: Nothing compares with Nick/Ellis which has come to dominate the fandom with their Ho Yay. And ever since the release of "The Passing" DLC, Rochelle/Francis has also been a target due to how the two interact (they both hate stuff).
Little Busters!: Rin/Riki is technically the official pairing of Little Busters, even if it's far, far more ambiguous than in most Key games, and certainly plenty of players ship it. But among the more serious fanbase, it's a lot easier to find Riki/Kyousuke or Rin/Komari fan art, and even Riki/Kurugaya is arguably as popular.
Lufia II: Rise of the Sinistrals has Tia and Dekar as a popular fan pairing, based on Dekar's heartwarming talk with Tia after Tia sees that Maxim is in love with Selan. The remake has Tia start dating Dekar after Maxim and Selan's wedding.
Despite Lux-Pain having a small fanbase, two of the main pairings that everyone can agree on are Shinji/Mika and Ryo/Hibiki. As for the main character himself, while he is shipped with everyone, the most popular pairing by default is Akira/Atsuki.
To put it simply, Akira/Atsuki has the mostShip Tease in comparison to the other potential love interests for Atsuki like Rui and Yayoi. Shinji/Mika is popular given that by pairing Mika up with Shinji, it greatly averts her being a victim of Die for Our Ship as well as evidence in the game that shows that she's moving away from Akira and getting close to Shinji. Finally, with Ryo/Hibiki, the fact that Hibiki is already confirmed to be in love with Ryo is one thing but whether or not Ryo has feelings for his best friend is up to debate although, there are some conversations that suggest that the feelings are mutual.
In Mana Khemia: Alchemists of Al-Revis, the only ending with a confirmed romantic implication (not counting Vayne-as-queen in Muppy's ending) was with Nikki. And yet there's a lot of fan support for Vayne/Jess.
Prior to Mass Effect 2, the two main fan-preferred couples for Mass Effect were Male!Shepard/Tali and Female!Shepard/Garrus. The two were so popular, BioWare made them both official options, and they still take up the bulk of Mass Effect fanfic.
There are loads upon loads of Ho YayMega Man X fans who ship X and Zero. And there's also Zero and Iris, and X and Alia. But X/Zero beats out the competition.
Samus/Gandrayda or Rundas are likely the most popular pairings that actually seem physically possible, mostly stemming from Gandrayda's rather affectionate dialogue and Rundas's general respectfulness. Samus/Dark Samus isn't far behind, even though the latter is a Humanoid Abomination and one of Samus's archnemeses.
Among the people who play this series who care about shipping, the majority prefer to focus on the extensiveHo Yay, which has lots more development, rather than the often underwhelming and Cartwright Curse-prone canon het romances. This may also have a lot to do with the extreme Camp content of the games, which attracts a big LGBT Fanbase that just doesn't care about the female characters as much.
For Metal Gear Solid, Snake/Otacon trumps Snake/Meryl (the CANON) by at least ten to one. The fact that you can actually kill off Meryl in-game to get a Ho Yay-ish ending with Otacon instead really doesn't help. Many fans are also much more interested in Snake and Fox's tragic, sadomasochistic relationship than in Naomi's attraction to Snake.
In Metal Gear Solid 3, most fans prefer to focus on the relationship between Snake and Ocelot than the one between him and EVA, and it certainly helps that EVA leaves Snake at the end while Ocelot goes out of his way to be with him again at the end, for inexplicable reasons.
Mortal Kombat: Most of the semi-canon pairings are pretty well-supported, but outside of them:
Judging by the fan art for Morenatsu, the most popular Hiroyuki pairings are with Tatsuki, Kounosuke, and Juuichi. Ironic, since this art existed before the patch which completed Tatsuki's and Kounosuke's route was released.
Neeshka was planned to be a canon couple, but it was cut from the game due to time restraints. It's not too hard to see where they intended to take it, and it's a lot more complete than Elanee's, even though it isn't, you know, complete.
In the same vein, Bishop is also a planned but cut romance option that fans seems to prefer over Casavir, partially due to the latter reminding them of Anomen, and partially because the former has heaps of Belligerent Sexual Tension with the female protagonist and, like Neeshka, feels more "complete" than the actual complete romance. Fans like them so much they made a mod that allows a "proper" romance, complete with an epilogue in Mask of the Betrayer.
People really like pairing Kai up with Oki in Ōkami.
Overwatch has an absurd amount of ships, all with varying degrees of popularity in the fandom. These are the most popular non-overlapping ships.
Tracer/Widowmaker had people shipping them ever since the very first cinematic trailer for the game came out. The pairing became even more popular when the Alive animated short came out.
Mei/Zarya has following, probably because of their cute in-game interactions and the fact that they are both frequently associated with snow and bears.
Pharah/Mercy is a popular ship owing to the fact that they are the only two characters that can remain air mobile and hence synergize very well. Blizzard added more fuel to the fire when one of their weekly brawls only featured these two together.
Soldier: 76/Reaper aka Jack Morrison/Gabriel Reyes, were basically inseparable best friends and are almost exclusively shown to be together in all official artwork of the time of the omnic crisis and Overwatch's golden years. While they canonly ended on terrible terms, many fans have leaped towards this ship because of the absolute goldmine of angst potential.
On the het side, the favorite Soldier: 76 ship is with Mercy thanks to the "Team Mom and Dad" interpretation of them, the old "Hurting soldier/ doctor" thing, and Mercy herself being a Launcher of a Thousand Ships
Ana/Reinhardt alternatively Grandma and Grandpa. It started from one of their pre-game interactions, which has a flirty tone to it. Many fans have found this endearing and cute. It also helps that their play styles synergize very well together.
Ana: Reinhardt, I must say you're looking quite well. This life must agree with you. Reinhardt: And you are looking as lovely as ever.
Roadhog/Junkrat's rough partnership, coupled with Roadhog's status as Junkrat's bodyguard, has resulted in a strong following. Come the Halloween event, one of the main screens featured Junkrat's Halloween counterpart hugging Roadhog's Halloween counterpart around the belly, smiling adoringly up at him.
Pokémon is a hard series to tackle, due to the numerous continuities and hundreds of ships. Shippers tend to have a habit of shipping protagonists with each other, or rivals and protagonists, leading to those being the top ships.
Hilbert or Hilda/N is quite popular for their games, more so than the two protagonists together (as is Cheren/Bianca from the same games).
Likewise, Cynthia/Dawn is almost as popular as said protagonist and either her rival or Lucas.
Interaction is not always required with common Pokémon ships. For example, Morty/Falkner has a sizable following, even though Morty and Falkner are never seen interacting with each other. (They can battle each other at the Pokémon World Tournament, but the player does not get to see it.)
If you search for a pairing with Calem or Serena, you will almost always find them paired together (though Serena and Shauna are also common).
When it comes to Kanto gym leaders, Erika and Sabrina get paired very often. They don't have much in terms of interaction but their contrast in personality combined with Erika being Ambiguously Gay spurs shippers on.
If you're looking at fanworks involving Eeveelutions, you're almost always guaranteed to see an Espeon and an Umbreon pair. They're almost never shipped with anything but each other. Usually the Umbreon will be male and the Espeon will be female. Though not nearly as common, Flareon and Vaporeon together is popular.
Pokemon in the same evolutionary group (for example, Gardevoir and Gallade or Pikachu and Raichu) have a tendency to be shipped together. Nidoran evolutions have been shipped in various canons but most others usually aren't in canon.
In the Professor Layton fandom, it's canon that the professor and Claire were in a relationship, and ten years later, even after her death, he still loves her dearly—of course, the fans prefer to ship Layton with Luke.
In the Resident Evil fan community, Chris/Jill has the most supporters since the firstResident Evil game's release. The second most preferred pairing is in fact Leon/Claire instead of Leon/Ada, although the latter has had a sharp rise after Resident Evil 4. For the main antagonist Wesker, however, he has lots of Wesker/Redfield shippers somehow.
Invoked, discussed, and deconstructed In-Universe in Senpai, Please Look At Me! In spite of the female protagonist canonically crushing on the titular Senpai, odds are that the player will prefer her best friend James instead due to him having a more well-defined personality, an actual name, a relationship with the protagonist that feels more meaningful than just a schoolgirl infatuation, and endings that are much easier to get than Senpai's. It turns out that Senpai himself is fully aware of this — if you try getting one of James's endings after getting Senpai's best ending, he erases James from the game so that he's the sole available love interest and repeatedly crashes the game in increasingly desperate attempts to make his interactions with the protagonist feel more organic and interesting. After his actions almost completely destroy the game, he breaks down and admits that he knows he's a dull love interest compared to James, with even the beta testers preferring James to him, and wanted to change that.
Beowulf/Eliza, which in spite of the fact them basically being polar opposites (one being a goofball BoisterousBruiser with a heart of gold and the other being an eons-old megalomanicial sociopath), has seemed to inspired a ton of fanart and fanfic. This is at least SOMEWHAT supported by the fact Beowulf's one of the few people that Eliza doesn't condescend to in her unique intro dialouge, and the respect she seems to have for the strong. A lot of people like to pair him off with Valentine, too, likely thanks to them openly flirting (or at least, the closest thing what to what could be considered flirting for Val) with one another in their unique dialouge
There's also a considerable amount of fanwork that that depicts Filia with either Painwheel/Carol or Squigly, thanks to her interactions with them in story mode.
While the Soul series is more preoccupied by violence and Rule of Cool than romance, subtextual or otherwise, fans nonetheless have a few:
Siegfried/Sophitia was one of the most enduring ships for a long time, until Hilde made an appearance and had an actual role in Siegfried's story. Now it's harder to determine.
Nightmare is often paired with Tira for people who are into a bit of Unholy Matrimony.
Mitsurugi/Setsuka is popular as well, especially seeing as she defeats him in a duel sometime between the events of IV and V and consequently drops her grudge against him. Although this ship often clashes with the older, more established Mitsurugi/Taki ship, which has a similar allure.
Kilik/Xianghua counts on a technicality. After four games' worth of Ship Tease and Unresolved Sexual Tension, from a Battle Couple moment at the end of the first Calibur all the way up to a (thankfully non-canon) bittersweetending in IV, there was no reason to believe that Kilik wasn't the father of Xianghua's daughter Leixia, especially when the girl was seen wearing his Dvapara-Yuga pendant. Naturally, many fans were none too pleased to learn that the two had parted ways between games and Xianghua went on to marry a Ming general named Yan Wujin and bear two children. Later on, it would be discerned that Kilik only left Xianghua in order to the protect the world she lived in, with strong implications that the two still love each other dearly. And guess who Xiba's parents are.
While Soul Nomad & the World Eaters has no Official Couple, Gig/Revya is the most popular. It helps that Disgaea games imply that their ending is canon if only because Revya travels with whoever has the highest affection for her at the end of the game and in Disgaea 3, Revya is traveling with Gig. Gig also doesn't stop talking about her in Disgaea 4 where he appears alone.
Ulala and Purge seem to be more popular than Ulala and Jaguar in Space Channel 5.
Star Fox: In Japan, Fox/Falco dominates fan expression. There's a lot of it in the West, too.
In Suikoden V, while (as is typical to the series) the Official Couple for the main character is never explicitly stated, the game beats the player over the head with indirect implications of a romance between the Prince and his bodyguard Lyon. However, it's popular among fans to pair him instead with his younger sister's bodyguard Miakis, a slightly older Genki Girl who's probably the most popular character in the game (or at least the most popular female character). This is particularly true in Japan, where the volume of fan art and fanfics implies that the Prince and Miakis are preferred over the semi-Official Couple by a roughly 3 to 1 margin.
Super Robot Wars generally avoids this between characters from licensed series, in hopes of preventing any unnecessary Ship-to-Ship Combat. However, there are some exceptions:
Female protagonist Setsuko Ohara of Super Robot Wars Z and Shinn Asuka in the same game is probably the most supported pairing, as it's one of the few that actually makes a lot of sense considering their close relationship in-game. And because it makes more sense than either of his pairings from the anime.
Many fans of Brawl are partial to the pairing of Solid Snake/Samus Aran. The game itself encourages the pairing through Snake's codec transmissions on Shadow Moses Island in which he talks to Otacon and Mei Ling about Samus; he says things like "Sounds like my kind of woman" and "But underneath that metal exterior beats the heart of a woman." The fact that the pairing is technically impossible outside of the Smash Bros. setting (not least because Snake doesn't even belong to Nintendo) deters pretty much no one. Before Brawl it seemed the preferred pairing was Samus and Capt. Falcon. One event in Brawl ("Unwanted Suitors") pokes fun at the pairing.
In Melee, Marth/Roy was incredibly popular (enough that it leaked into the actual Fire Emblem fandom). In Brawl, Roy was replaced by Ike both in the roster and in that ship. It remains to be seen how the inclusion of Robin and Lucina (and Corrin via DLC) as well as Roy's return (also via DLC) in the fourth game will affect the Fire Emblem ships.
Tales of Destiny 2: Judging by the amount of Harold/Judas fan art on Pixiv, Judas is the only person anyone ships Harold with and vice versa. Though the fact that Judas is Leon complicates the issue, as Leon/Stahn and Leon/Marian are both very popular.
Fans in the West prefer Senel/Chloe to the heavily implied Senel/Shirley. After all, Senel and Chloe spend most of the game getting to know one another and discovering what they have in common (though, ironically enough, their similarities are used in-game as the chief reason they can't end up together). Meanwhile, Senel introduces Shirley as his sister, was in a relationship with Shirley's actual sister, and when he spurns Shirley for her dead sister, she turns into a Woobie, Destroyer of Worlds who almost floods the world.
In Tales of the Abyss, Luke/Tear. One of the few examples in the entire Tales series where the Fan-Preferred Couple (Ho Yay pairings notwithstanding) is completely supported by the canon. In the case of side couple Peony/Nephry, Peony's canonically still pining after her even after ten years, but there's a lot more visible shipping activity for him and Jade. (Weirder still if you consider that Jade is Nephry's brother.)
Team Fortress 2: Any coupling outside of RED Spy/BLU Scout's mother and possibly Demoman/the opposing Medic's wife is based in Fanon, but the highly suggestive lines the Heavy has leads to Heavy/Medic being the most popular. Valve even ship teases these guys with the "Beaux and Arrows" achievement, which you get when you pin a Medic to a Heavy using an arrow, and the Medic-only Gentleman's Ushanka, which mentions the hat would match with the Heavy's ushanka.
For Togainu no Chi fans, Shiki/Akira easily beats all other pairings in the English-speaking fandom. Granted, it is not more or less canon than any other pairing in the series. Meanwhile in Japan, Keisuke/Akira is very popular among the fans.
Until Dawn comes with a group of 8 young characters who are conveniently paired off with each other. Still, a lot of people like the idea of Mike and Samantha being together instead of with Jess and Josh, thanks to their statuses as the top Badasses of the group. The game seems to encourage this by sticking the two in situations where they save each other and, if both survive, shows them clinging to each other as they watch the lodge go up in flames.
Chris and Josh (nicknamed "Climbing Class") is also a popular ship, on account of the two being Childhood Friends.
Jess and Matt have their shippers, too. They're dating Mike and Emily respectively, but are separated from them halfway through the game, culminating in the two of them escaping the mines together if they both survive to the climax. That plus the facts that Matt's relationship with Em isn't exactly harmonious and that Mike himself is part of a different Fan-Preferred Couple (as mentioned above) lend to people liking the idea of seeing them together.
Fans of Valkyria Chronicles vastly prefers the pairing of Selvaria Bles with Johann/Oswald the Iron. Considering what kind of dick Maximillian (the one Selvaria is canonically interested at) is, it should come as no surprise. Radi Jaeger is sometimes a decent substitute, too.
The designers poked fun (or just rubbed salt in the wound, depending on your view) at the Ship Sinking during Thrall and Aggra's in game wedding. After the wedding concludes, if you stick around long enough, you can catch Jaina openly sobbing.
Another example would be Wrathion/Anduin, due to their massive amounts of interaction in the game and the novel War Crimes that just screams Opposites Attract. Even some Blizzard's employees ship them to the point that the writer of the novel had to confirm that they're just "good friends." No one really believes her.
It's pretty much a common knowledge in the Wild ARMs 2 Japanese fandom that Lilika deserves Ashley much more than Marina does.