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.
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.)
In Japan, there's a ludicrous amount of Rita/Raven fan art, especially on Pixiv, probably owing to their dynamic seemingly having Slap-Slap-Kiss potential.
For the West, Flynn/Yuri and Estelle/Rita have the most amount of fan work by far.
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.
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 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).
Among the playable units in Blazing Sword, there's Erk and Priscilla, helped by the fact that this is her only romance option with a happy ending.
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 for a couple of exceptions, mostly Basilio/Flavia and Maribelle/Lissa, both of whom have a very solid relationship in their Supports and in story scenes.
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.
Since his announcement for Smash Bros 4., Little Mac/Samus has been gathering some steam, because Little Mac's reveal trailer compares the height difference between him and Samus (who is much taller). Most people would agree that Wii Fit Trainer is also a fitting choice for him.
In Melee, Marth/Roy was incredibly popular (enough that it leaked into the actual Fire Emblem fandom). In Brawl, Roy is replaced by Ike both in the roster and in that ship.
Jon Talbain and Felicia have appeared in more fan art than can be counted. This being said, there's not much to link them in the games, though the comics and OVA can be seen as evidence.
Demitri and Morrigan. It's not nearly at the height of Felicia/Jon, but it does have a good share of vocal supporters. The fact that it's implicitly official in the OVA doesn't hurt either.
Donovan/Hsien-Ko was likely started due to their interactions in the anime.
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.
Kairi from Kingdom Hearts 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.
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 Persona 2, the most popular pairings depends largely on which game the fans are talking about. The most popular pairing of Innocent Sin, the first of the duology, is most certainly Tatsuya/Jun, while in Eternal Punishment, the second game in the duology, it seems to be Tatsuya/Maya. The third option, Tatsuya/Lisa, hardly has any supporters at all. The fun fact behind this is that these are the pairings that are pushed a bit by each game, but there are quite a few fans of the other pairing in each game. The other weird mention is that Tatsuya is the same between these two game's universes, while the love interests are not. It is still a hot debate in the fandom to this day who Tatsuya actually loves, but considering he's a walking mess of complexes, he's not likely to say it anytime soon.
Although doesn't have an official couple (thanks in part to the fact that you can date everyone), the Protagonist usually seems to end up with Naoto in fan works, to the point that the aforementioned spoiler is practically entering It Was His Sled territory. Yukiko and Rise are in a dead heat for second, with Yukiko apparently winning by a slight margin.
Fans of the older characters in the game tend to ship Dojima/Adachi. A lot. Never mind that Adachi is the Big Bad of the game and tried to get Dojima's daughter killed. And all of this started when Adachi tried to rape two women. It's said that Adachi/Nanako has a particularly big pairing in Japan, also. Nanako is a seven year old, by the way.
Recently, more and more people are starting to ship Kanji/Naoto—aka "Kannao"—as a serious ship instead of something played for laughs. On Japanese fan work sites such as Pixiv, the number of Kannao doujinshi, artwork, and light novels are now outpacing that of Protagonist/Naoto.
Persona 3: The female Protagonist's most popular pairing is Shinjrio by a huge margin, since completing his Social Link is the only way to save him from his Plotline Death.
Metal Gear Solid, my god. Among the people who play this game who care about shipping, 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.
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.
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.
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?
Aveyond 3 gives us Edward/Mel. While it's possible to put them together in individual gameplay, the canon pairings are Edward/Stella and Mel/a descendant of Lars who doesn't appear in the game. It's not helped that in the trailer to the third chapter, it shows the Edward/Mel prologue, thus implying that Edward proposing to Mel was the canon ending of the second chapter.
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 one almost everyone seems to like, though, is Gumshoe/Maggey. Probably because it's pretty much canon, and pairing the two Butt Monkeys together is cute anyway. Almost everyone seems to like Diego/Mia (which is canon), and Ema/Klavier from Apollo Justice.
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.
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.
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.
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...
While Ragna/Rachel is getting more attention there is a following for Carl/Rachel mainly through their interactions in the first game (and to a much lesser extent the second).
Jin/Noel has a rather healthy fanbase.
More recently, Kagura/Makoto has been gaining some traction, based on their interactions in 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.)
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).
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 a sharp rise after Resident Evil 4. For the main antagonist Wesker, however, he has lots of Wesker/Redfield shippers somehow.
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 fangirls prefer to ship Layton with Luke.
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.
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. Also, Silver/Lyra has a strong following.
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.)
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.
While Frozen Essence lets Mina hook up with no less than five characters, the one who comes the closest to being a "default option" for her is Rune who she needs to pursue to get the True End. Naturally, the majority of players prefer Mina to be with Caius or Zareh instead; the former because All Girls Want Bad Boys, the latter because of him having been in love with Mina far, farlonger than anyone else.
For Assassin's Creed I, Altaďr Ibn La'Ahad with Malik a-Sayf, which didn't stop even after the PSP game Bloodlines paired Altaďr with Maria Thorpe who'd been the unnamed female Templar in ACI.
Assassin's Creed II and its sequel has Ezio Auditore da Firenze with Leonardo da Vinci, and confirmed the Altaďr/Maria pairing... not that that, or the fourth game pairing Ezio with Sofia Sartor has stopped the shippers.
Ditto for there being far more Shaun Hastings/Desmond Miles out there than the canon-suggested Desmond/Lucy.
The most popular Assassins 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.
Despite Golden Sun 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.
In 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 his 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.
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.
Every single couple has its fair share of fans in Avalon Code, but Anwar/Tia has a very notable fanbase. On the flip side, Yumil is often paired with Dorothea.
Ulala and Purge seem to be more popular than Ulala and Jaguar in Space Channel 5.
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.
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.
The Japanese Bahamut Lagoon fandom ships Byuu and Frederica despite there being little evidence, and Byuu and Yoyo, who broke up in-game.
For some reason, Hiroshi/Takuro is fairly popular in Ao Oni.
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.
It's pretty much a common knowledge in the Wild ARMs 2 Japanese fandom that Lilika deserves Ashley much more than Marina does.
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.
Yaoi Fan-Preferred Couples abound as well. Probably the most popular examples include Fou-lu/Ryu which is technically a selfcest pairing in IV, Ryu/Bosch in Dragon Quarter, and Elyon/Jesuit in DQ.
Star Fox: In Japan, Fox/Falco dominates fan expression. There's a lot of it in the West, too.
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).
In Dishonored a popular theory is Corvo is the lover of the Empress and possibly even the father of Emily.
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.
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.
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.
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.
Pit and Viridi from Kid Icarus: Uprising could count as one, if the fan art and fanfiction have anything to say about it.
Dark Pit and Phosphora are often shipped together... for some reason.
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.
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.
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.
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.