Pretty much every game of the Aveyond series has this
Ahriman's Prophecy's canon is Devin/Alicia, but he is more popularly paired with Talia, his Childhood Friend whom he has more interactions with. It should be noted that Devin/Talia is canon in AP, but that things changed between games and Devin ended up with Alicia afterwards.
In Aveyond 1, the number of Lars/Rhen fans outweigh the canon Dameon/Rhen fans, to the point that an official patch was released to add a bonus ending where Rhen goes back to Veldarah with Lars after the adventure is over to teach at Shadwood Academy.
For Aveyond 3 most fans ship Mel/Edward, since their early dynamics resemble a classic Belligerent Sexual Tension, and their in-game roles seem a set-up for them to eventually hook-up. However, while the gameplay allows Edward to marry Mel, Word of God confirms that his canon love interest is Stella.
Darkstalkers: Played with in regards to Demitri/Morrigan. While it's teased quite a bit in the games, and actually ends up being canon for both the OVA and manga (possibly as a result of fans latching onto the ship), many other fans prefer the Les Yay vibes Morrigan has towards her "youngersister" Lilith or even pair her up with Jedah—the former being aprominenttheme in their interactions ever since Lilith's debut and the latter ship seeing gaining some additional tractional due to the strange amount of concern Morrigan shows Jedah in Marvel vs. Capcom: Infinite. Demitri/Morrigan still appears to be the more popular ship, but the others have been steadily growing in popularity. Morrigan being a succubus with Anything That Moves tendencies likely accounts for this.
In the rebootDmC: Devil May Cry, Vergil/Kat were the designated canon pairing, yet far more people prefer Dante/Kat due to the latter's far better treatment of Kat as well as being fully transparent with her regarding his intentions.
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 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.
Dragon Quest V really wants the player to choose Bianca as the Hero's bride, but many of the remake's players picked Deborah as the protagonist's wife for her looks, Hidden Heart of Gold (which becomes more obvious late in the game in party conversations) and for having some of the funniest dialogue in the game (such as when she tells the priest blessing their wedding to hurry up with his speech).
Dragon Quest XI: Although Hero/Gemma is canon, Hero/Jade is a very popular ship. Despite the stated tone of their relationship, many feel their tender moments together edge into amorous territory. Not to mention the prince of Dundrasil and the princess of Heliodor making for a natural match, which is lampshaded in the Switch version. Not to mention, before the events of the game, Jade (as a child) only knew the Hero as a newborn baby, so seeing the present-day Hero, a virtual stranger, as her sibling-figure doesn't seem to make much sense. As of the Switch version, the player can choose to make it a reality.
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.
On a good number of sites for Final Fantasy VI, fics and fanart for Terra/Celes rival those of the canon Locke/Celes; there's even at least one fangame that rewrites the plot of the fourth game to feature the two. This is despite the fact that Terra and Celes only interacted about twice canonically, and are rarely together even outside of that except when the entire party is in unison (Terra vanishes not long after Celes joins the party, and returns just in time for Celes to leave again, and by the time they're both playable again, the cast size has hit double digits). Fans of the pairing tend to cite their strong parallels and contrasts, their status as dual protagonists, and their potential for intriguing interaction. (This may be paired with seeing Locke asa bit of a creep.)
From the Terra Battle crossover with Final Fantasy XV, Noctis/Sarah has a fanbase of it's own. Especially due to Sarah's actual shared chemistry with Noctis which is aided by the fact Sarah actually gets to interact with him alongside having an actual personality.
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.
Honkai Impact 3rd: Kiana and Mei are the most teased pairing, but recently it seems like the fans prefer Kiana and Fu Hua's relationship. With a large amount of fanmaterial, particularly on the Chinese fanbase's end of things, dedicated to the pairing. It doesn't help that in 2019 almost every event had the two paired off with one another, and 2020 kicked off with an event where the first thing the player sees is a scene where Fu Hua is giving Kiana a Lap Pillow.
Kingdom Hearts: Kairi is semi-officially paired with Sora (they both shared 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.
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 Legend of Zelda: Breath of the Wild, Link/Prince Sidon is an explosively popular ship, with more art, fanfiction and posts in general being made about Link and the fishy prince hooking up than any other couple.
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.
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 between Vayne and Nikki. And yet there's a lot of fan support for Vayne/Jess.
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 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.
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.
With Metal Gear Solid: Peace Walker, when fans make art or stories involving Dr. Strangelove with anyone, they find her doomed love for TheBoss far more interesting than her rather sudden pairing with "Huey" Emmerich. The fact that he would end up killing her years later as revealed in Metal Gear Solid V: The Phantom Pain further reduced any interest in this pairing.
The male main character and Neeshka. The majority of fans seem to prefer her to the canonical Elanee. 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, the female main character and Bishop is also a planned but cut romance option that fans seems to prefer over Casavir, partially due to the latter reminding them of the unpopular 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.
Spending all the game in the form of a wolf hasn't stopped people from shipping Ammy with the lighthearted and mysterious, Waka. It helps that the two were close comrades in the past and Ammy's true form is that of a fair maiden.
Onmyōji: Even though Seimei is quite obviously Ship Teased with Yaobikuni in canon, the vast majority of fans like to pair him with Hiromasa, reason being that their corresponding historical figures are frequently portrayed as having a close relationship in other works.
Tracer/Widowmaker had people shipping them ever since the very first cinematic trailer for the game came out, and only increased in popularity when the Alive animated short followed. Even though Tracer was eventually revealed to be in a relationship with Emily, that did nothing to deter the fans.
Reaper/Soldier: 76 is far more popular than the latter's canon partner, Vincent. Partially due to the relationship being a recent reveal and the abundance of lore already in the series as both were major members of Overwatch during the Omnic Crisis, and were described as the best of friends. It's helped by the fact they were explicitly said to have loved each other in the past. What this type of love is, however, is not explicit.
The most popular pairing outside of those involving the protagonist by a large margin is Ryuji and Ann. This is helped by both of them having a lot of Ship Tease moments in the game, as well as Ann's English voice actor personally liking the ship. The pairing was popular enough to start a rumour shortly after the game released in Japan that Ryuji would hook up with Ann if the player didn't romance her.
Even though the game lacks any Gay Options for the protagonist, that hasn't stopped Joker/Akechi from enjoying a strong following within the fandom, especially in Japan, to a point where fans joke about it being the game's Official Couple. This is helped by Akechi canonically having feelings for Joker and as a result, his Confidant is dripping with subtext between the two. The player even gets an option to greet Akechi with the line "Honey, I'm home." when returning to Leblanc at one pointNote In the original Japanese version, Akechi greets the protagonist with "おかえり" ("okaeri"), short for "お帰りなさい" ("okaerinasai"), which is mostly used by someone to greet another to a place they both regard as "home" or a "home base". Likewise, the "Honey, I'm home." line is instead "I'm home", with Akechi chastising the protagonist for coming home late if the player chooses it.
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.
Rainbow Mika/Hakan also has a surprisingly large following. Like the above example, Hakan is canonically married.
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.
Rean and Crow is easily the most popular pairing in the series, significantly more than Rean and Alisa, due to having the most natural chemistry and interactions.
In canon, Juna is one of the potential love interests for Rena. Fans, however, are more likely to pair Juna with her classmate Kurt, despite the two intended to be written Like Brother and Sister.
Hyde Kido of Under Night In-Birth has alot of girls in his life, but he's primarily promoted as being in a tag team with Linne and is confirmed to be attracted to Orie. The fans, however, would rather ship him with Vatista instead.
Undertale: Sans/Toriel due to their shared love of jokes. This is despite the fact that Toriel may still be married to King Asgore, whom she used to be soulmates with, but is at the present extremely pissed with him for trying to destroy the human race (and killing 6 human children in the process of said plan). Fans interpret Toriel as already divorced from Asgore, and want Sans and Toriel's mutual love of jokes to evolve into more.
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.
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.
Valkyrie Profile: The resident Draco in Leather Pants, Lezard, is unquestionably the favored love interest for main character, Lenneth. He's one of the most dedicated Yanderes you'll come across, but unusually for a male Yandere, the fans eat it up. It's even funnier since Lenneth actually has a genuine love interest- Lucian- with story significance and an arc and is devoted to Lenneth in his own more wholesome way but good luck finding fans who even acknowledge him, let alone ship the two. Lucian just comes across as bland by default and in the face of the much more interesting Lezard he's outright forgettable.
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.
The World Ends with You: Joshua and Neku have an enormous following among the fanbase. Where to begin? In game, Joshua blatantly flirts with Neku more than once, and Shiki even implies she thinks they might be a thing at one point. Joshua's small role in the manga is also dedicated to his implied infatuation with Neku. While the game and its fanbase generally isn't focused much on romance, there is a staggering amount of fanart and fanfics on this pairing while not much else for other pairings exists.
In the Yo-Kai Watch fandom, some fans prefer to ship the hero, Nate, with Yokai Watch 3 heroine, Hailey, instead of the previous heroine Katie, whom he canonically marries in the Time Skip series Yo-kai Watch: Shadowside. Part of this is because Hailey has Yokai friends like Nate does and they spend more time interacting in the series. Meanwhile, Katie is Schrödinger's Player Character, and does not get to have Yokai friends in the same canon as Nate.