The most popular Hellsing couples are Alucard/Integra, Alucard/Seras, Pip/Seras and Alucard/Walter (the young or Dark Walter versions...which is ironic since canonically Alucard refers to Walter's natural, elderly body as being trillions of times more beautiful than his artificially youthened one).
Walter/Girlycard. Sometimes, the fans make Alucard take his girl form (aka Girlycard) in Alucard/Walter stories.
Aside from the age and incest hurdle, Sasami from Tenchi Muyo! is big with fans for being the most subdued and overtly normal — or at least sane — girl in the show (in very general terms). In fact, before the Great Crash, this page was called "Sasami Syndrome". Word Of God has it that Sasami will marry Tenchi eventually. Because everyone else will, too. Even then, however, many fans feel that Sasami alone - or any of the girls - would be preferable to Status Quo Is God.
Kiyone and Tenchi is extremely popular with fans too, for same "overtly normal or at least sane" reason as Sasami without the incest and pedophilia problems. Unfortunately Kiyone appeared only in spinoff media, Tenchi Universe hinted heavily towards Tenchi liking Ryoko, Tenchi in Tokyo ended ambiguously without a Word Of God, and, most importantly, Kiyone was the only girl, perhaps in the entire franchise, who showed no romantic interest in Tenchi, which just made fans want it more.
Soul and Maka from Soul Eater, though the same can be said for all of the meisters and their weapon partners. Kid/Crona is also very popular, especially on deviantART. Although meister/weapon pairings are very popular, Soul/Maka seems to be the biggest faction, with at least three separate deviantART fangroups.
There's also a significant faction of Kid/Maka, Kid/Soul, Maka/Crona, and Stein/Spirit supporters that should not be over-looked.
Anyone familiar with the conventions of Shōnen would tell you that the obvious candidate for the title character's final love interest was Sakura, the Tsundere object of his comical one-sided affections. Yet for years of the manga's run, most of the fandom rooted for Naruto to turn around and notice Shrinking VioletStalker with a Crush Hinata. Despite the relative lack of actual interaction, NaruHina had been popular enough to get plenty of Ship Tease in Filler, a date in a High School AU bonus feature and a canon-defying Relationship Upgrade in a video game adaptation series. Only after over 5 years of running time the manga started treating it as a serious possibility. It holds; the epilogue reveals that they married and had two children together, and the final movie, which is set two years after the end of Naruto and Sasuke's final fight, is the canonical tale of how they fell in love.
Naruto/Sasuke enjoys all sorts of support and homage, especially on fanfiction.net and its ilk, even though it has already been well-established that Naruto is straight and Sasuke is homicidally insane. To be fair, Naruto's disproportionate obsession with "saving" Sasuke does raise an eyebrow or two, and there are plenty of things occurring in the manga that would have made the ship all but canon a long time ago if it weren't for the fact that Shonen Jump would never allow a homosexual couple as endgame. Among the rest of the generic Ho Yay galore, Kakashi/Iruka stands out in popularity, with Genma/Raidou and/or Izumo/Kotetsu as popular Ship Mates.
Shikamaru is so frequently paired up with Temari (by fans in Japan, the West and pretty much anywhere the manga is known) that many assume it is already canon, even though they haven't technically gone on a date (though Naruto incorrectly assumed they had when he saw them walking together just after the Time Skip) and another girl named Shiho has shown strong romantic interest in Shikamaru. The series does hint heavily at something being there- they keep getting Ship Teasehalf-invisible to the naked eye- and Word Of God agrees there is something between them, but seems to suggest it's just not important enough for us to get to see it happen on-panel. Which hasn't stopped fans from anticipating a Relationship Upgrade.
Tsunade and Jiraiya before the latter died. The latter's love for the former is canonical but unrequited, both before she met Dan, her canonical boyfriend, and after Dan died.
The Grand Finale revealed the final couples among the Konoha 11: NaruHina, SasuSaku, ShikaTema, SaiIno. By the looks of it, the majority of the fans got their way.
Fans of Da Capo are rather divided about who Jun'ichi should have ended up with, but most think Kotori would have been a much better match for him than Nemu for various reasons, among them not being a Tsundere or his adopted sister. Unfortunately, the sequel reinforced the official pairing by featuring Jun'ichi and Nemu's granddaughters. (An alternate-universe OVA was released in which Kotori wins. Kotori must have been pretty popular.) In the original VN, Nemu has almost an unrecognizable personality if you're only used to her in the anime (she's far less bitchy and far more empathic and likable). She was undoubtedly the favorite of the majority until the anime adaptations.
Kasumi/Dr. Tofu is a surprisingly common ship. Admittedly, it was one of the first genuine-seeming romances hinted at in the series, but Word Of God states that Tofu's feelings are one-sided, which is hinted at in canon by the fact that Love Makes You Dumb and Love Makes You Crazy apply to Dr. Tofu to such an extent that Kasumi is honestly unaware that he acts any differently normally.
In Japan the reason that the anime was shown out of order was because they wanted to introduce Shampoo earlier to boost ratings since she was the fan favorite fiancée in that country where Shampoo/Ranma was the most wanted pairing at the time.
Many fans find the more emotionally expressive pop idol Seiya Kou from the Stars season to be a much better match than the more subdued Mamoru because Usagi and Seiya's personalities mesh well together. The fact that Seiya is actually female is not addressed by the series, though the series conveniently keeps Usagi painfully oblivious to Seiya's feelings up until the end of the series. This is also not helped by the manga having Seiya love Usagi from afar (and even forge correspondence from Mamoru since Usagi was still in denial over him dying in front of her) and the anime actually using her as a Replacement Love Interest when Mamoru was Put on a Bus.
There are a lot of fans who give in to the lesbian-oriented subtext supposedly in the show, the manga, and the live-action version. The most popular non-canon couples are Minako/Rei, Makoto/Ami and Hotaru/Chibiusa. Of course there are many, many more variations of this, especially when one includes the het possibilities.
Many of the fans who watched the Rurouni Kenshin prequel OVATsuiokuhen/Trust and Betrayal or read the corresponding Remembrance arc in the manga came to prefer his lost love, Tomoe, over his Second Love, Kaoru, in spite of the teeny-tiny problem of Tomoe being dead by the time Kenshin meets Kaoru.
Many Hot Gimmick fans prefer Hatsumi to have ended up with her (adopted) brother Shinogu rather than Ryoki, given Ryoki's treatment of Hatsumi. And in the novel, Hatsumi actually does end up with Shinogu.
Many Fushigi Yuugi fans prefer to pair Miaka with Tasuki instead of Tamahome.
Suboshi is far more popular a love interest for Yui than Yui's canon boyfriend, Tetsuya.
While Ken/Miyako (Ken/Yolei) wound up canon in the finale, there was very little actual development between the two other than Yolei mentioning her having a crush on him. Unsurprisingly, couplings of either with someone else usually have more fan support. Takari (Takeru/Hikari) also ended up as this since it already had a large fandom from when it was a popular Toy Ship in the first season.
Not that the writers handled the Tai/Matt/Sora relationship all that well after they got together in the series; discussions often point out how, while Matt and Sora are clearly the parents of one another's children, the epilogue deliberately refrains from saying they got married (leaving the explicit statement of their marriage to All There in the Manual) and keeps them from interacting much at all — in clear contrast to Ken and Yolei. The nitpicky may also bring up how Sora both addresses Tai first and dodges behind him in Diaboromon Strikes Back, when Matt was right there.
Digimon is good about those. Rukato (Ruki/Rika and Takato) fans are a large part of the fanbase who think Ruki is a better match for Takato then Canon Love Interest Juri/Jeri. They mostly say that that is because Ruki and Takato have a "Hot-headed girl x cool-headed guy" chemistry, or even Slap-Slap-Kiss.
Not that Takato and Ruki (or Ruki and Jian)note Okay, this guy has more Spell My Name with an "S" going than simply having a different name in the US. His Japanese name, Jenrya Lee, is the Japanese way of writing the Chinese name Jianliang Lee. This wasn't a widely known fact when the series was new, so Jenrya and Jen are names that frequently appear in fandom. His dub name is Henry Wong. And of course, there's First Name Basis being more intimate in Japan than in the west - "Lee-kun or -san is his most common onscreen Japanese name. So Henry, Jenrya, Jen, Jianliang, Jian, and Lee all refer to the same guy. ever got along too badly. And the Ship Tease with Ryo was mostly him hitting on her as part of their rivalry, and stunted by his few sporadic appearences in the latter third of series making it hard for most viewers to get attached to him.
"Hot-headed girl x cool-headed guy" probably best fits Ruki and Jian, as that pairing was wildly popular in the Japanese fan community. In canon, Ruki got a lot of Ship Tease with Ryo, but you'll find more fanwork to Ruki and Jian ("Leeruki" as the Japanese fans called it) than for Ruki and Ryo.
There's the popular pairing of Ruri/Akito in Martian Successor Nadesico. This is also kind of aided by the fact that their seiyuu, Omi Minami and Yuji Ueda, are married in real life.
Strawberry Panic! fans will often hate Amane for two things: taking away their beloved Hikari/Yaya Coupling and being a Bifauxnen. It doesn't help that many viewers, and several reviewers, who weren't even in a Shipping mindset, found the Hikari/Amane romance subplot to be bland and forgettable.
The most popular pairing in Slayers fandom used to be Lina/Zelgadis, given that both are level-headed and intelligent (despite the fact that Zelgadis cannot stand Lina at times), as opposed to the canon Lina/Gourry. Nowadays, it has a rather small following. This might have something to do with Amelia becoming less hated over the years, partly due to character development. Other official works have noted this - the Light Novel series artist now draws Zelgadis and Amelia together, and several manga adaptations, namely the manga version of the fifth anime season, has a massive Ship Tease in regards to them.
The amount of Domon/Allenby shipping in G Gundam is rather amazing considering that this show came before the series that allegedly attracted all the stereotypical shippers to the franchise. Proof that Love Triangles can survive and thrive even in a fairly straightforward shounen kung-fu-with-giant-robots show. The fact that Allenby herself is a Shipper on Deck for Domon/Rain, and the one who convinces Domon to tell Rain how he feels, doesn't seem to have gotten in the way.
The manga adaptation played up Allenby and Domon's teasing; the artist made it clear in an interview that he preferred Allenby to Rain.
Natsuki/Shizuru is also overwhelmingly popular. There are more Natsuki/Shizuru fanfics in the Mai-Hime section of fanfiction.net than there are all other stories combined. They are a couple in Mai-Otome, but that's a different continuity.
CLANNAD was extremely obvious about pairing Tomoya and Nagisa. Didn't stop many, many people from wanting to pair Tomoya with Kotomi or Tomoyo.
Ulquiorra/Orihime, big time. This was specially jump-started in the infamous "slap scene" (where Orihime snaps on Ulquiorra after he insults her friends), and then it went on LOTS of Foe Yay/Mind Game Ship-like Ship Tease. Needless to say, their finalscene pretty much cemented them in that position.
Uryu/Orihime was especially popular during the Soul Society arc, as the two teamed up and worked together for the majority of the arc. It didn't help that this was the point Orihime's character transitioned from The Ditz into being far more serious and empathic; this resulted in her showing a deep care and concern for her good friend Uryu (especially when he ended up facing Mayuri) that several interpreted as a product of deeper feelings (though later on it was revealed to simply be Orihime's nurturing personality). Needless to say, poor Orihime's silent confession to Ichigo was considered a Face-Heel Turnfor some shippers, who assumed that they'd be paired off and/or that Orihime owed Ishida romance.
Alternatively, fans also liked pairing Ishida with Mayuri's "daughter", Nemu, after he stood up for her. There's a fair amount of fan art depicting them as a couple and fanfiction which either has Ishida "rescue" her from Mayuri, or simply sweep her off her feet by helping her learn how to feel emotion. The anime also seemed to like the idea and gave them extra scenes together, which weren't in the manga, such as when Nemu gives him the Quincy Bangle during the "Bount Arc".
Other popular pairings include Hitsugaya/Hinamori (despite this being a confirmedLike Brother and Sister relationship), Hisagi/Rangiku, Gin/Rangiku, and/or Urahara/Yoruichi (the latter are childhood friends who clearly are/were very close, but no indication is given one way or the other as to whether romance is involved). Slash fans have their share of preferred ships as well, such as Ichigo/Renji, Ichigo/Uryuu, Ichigo/Grimmjow, or Ulquiorra/Grimmjow. The most prominent yaoi ships are Ikkaku/Yumichika and Kyoraku/Ukitake. Neither pairing exists in the manga, but the Ikkaku/Yumichika pairing in particular is given almost as much fillerShip Tease by the anime as they give IchiRuki. Almost all yuri fans support Yoruichi/Sui-Feng.
A certain reveal in the final arc caused Zaraki/Unohana of all things to explode.
A lot of Gundam SEED and Gundam SEED Destiny fans still scoff at the official pairings and think Kira/Flay, Athrun/Cagalli and Shinn/Stellar are a lot better. In Shinn and Kira's cases, it appears to be a 50/50 even split.
The case of Athrun/Cagalli was certainly a peculiar one, as they were a canon pairing in the first series and the beginning of Destiny, but through a series of strange events (both in the series and in RL), they ended up dropping out. Even so, fan demand was apparently so much (especially when the pairing wasn't reestablished in the revamped Destiny finale) that Mitsuo Fukuda, the director for both series, ended up putting together a few Athrun/Cagalli themed AMVs in response.
Roy/Riza ("Royai") of Fullmetal Alchemist seems to be of the "set it up as fan-preferred for extra credit when it becomes official" variety, with many other charactersacknowledging it. But the true Fan Preferred Couple of the series is Roy/Ed, which is unsurprisingly popular with slash fans (especially among fans of the first anime, where there was far less Royai build-up), even with Ed being in an Official Couple with Winry by the end of the manga/Brotherhood.
Overall, the whole issue of shipping is one of the big divides between fans of the original anime and those of the manga/Brotherhood; fans of the latter overwhelmingly prefer the various Official Couples, whereas the former focused less on romance and had a more ambiguous ending, leaving fans to draw their own conclusions. (For example, part of the reason that Roy/Ed was so fan-preferred is that the first anime's Het shippers were fiercely divided over whether Ed belonged with Winry or Rose, a much more important character in the 2003 anime continuity.) However, overall, Roy/Ed remains the most popular ship when one crunches the numbers on fanfiction and fanart sites, especially in the Japanese fanbase.
Elricest (Alphonse and Edward) is far, far more popular with 2003 fans than in the manga-verse. The ending to the series, with them being on the other side of the Gate away from their friends and in turn from love interests, only helped.
Though shipping Edward with Winry was exceedingly popular for 2003 fans it's also very common to pair her with Sheska. The same reasons above only made people ship it more, even some Edwins fans.
Sidekicks Yamamoto and Gokudera are arguably the most popular ship among American fans. Dino/Hibari and Mukuro/Hibari fans are also abundant.
A lot of people who have read the Haruhi Suzumiya novels are of the opinion that Kyon/Yuki is the perfect couple. This can be attributed to the 4th novel, Disappearance, which focuses majorly on Yuki and Kyon, as well as the fact that Haruhi tends to go Out of Focus, while Yuki becomes more focused on, all combined with an utter lack of any major Haruhi/Kyon hints. The fact that the author himself has said Yuki is his favourite character may also help. It may also help that Yuki is beloved by an enormous portion of the fandom, individuals at worst not expressing any interest in her, while Haruhi, though popular as well, has acquired a significant force of haters due to the more abrasive and violent portions of her personality.
Most Lucky Star fans prefer to ship Konata and Kagami, and there have been some slightShip Teases, mainly on Kagami's part.
There have been some similar Les Yay debates over Azumanga Daioh, mainly involving Shrinking Violet Sakaki. The most popular Fanfic pairings for her seems to be with Kagura. Chiyo/Osaka seems to be another favored pairing in the fandom.
The Tomo/Yomi pairing is outright considered Fanon.
As is Yukari/Nyamo, with many assuming the once mentioned "Love Letter" was to Yukari from Nyamo.
The Higurashi no Naku Koro ni fandom is split on who Keiichi should be with, with all of the girls claiming a share of fans (Rena and Mion being the most popular). Rika/Satoko is far more popular than Rika/Hanyuu or Satoko/Hanyuu.
From Ashita no Nadja, at least half of the fanbase will tell you that Kennosuke is that much of a more fitting match for Nadja. It helps that Nadja's Love Triangle-y canon interest on Francis/Keith (Black Rose) is mostly based on a "he saved me, therefore I love him" reaction, while her friendship with Kennosuke was actually developed and detailed.
Although by far one of the most popular couples in D.Gray-Man, the mind-numbingly obvious pairing of Allen and Lenalee has accumulated a fair amount of haters. Most of the remaining in the fandom are proud Yullen (Kanda/Allen) fans because of a "hate/love" appeal.
Quite a few Genshiken fans would love to see Madarame and Saki at least try to get together. Sure, Madarame seems to have a disadvantage compared to Kousaka in the looks department, but he and Saki seem to be a much better match when it comes to temperament. They also like to tease each other a bit too much for comfort.
Although the canon pairing (in the manga, at least) is Tamaki/Haruhi (which is still fairly popular), many fans pair Haruhi with Hikaru (who also has romantic feelings for her, although they're one-sided). The anime kept all possible pairings open by ending with Haruhi not romantically involved with anyone, which was probably a smart move on their part.
Hikaru/Kaoru is the most popular pairing on fanfiction.net, despite it being the least likely of all the pairings to become canon.
From the same website, Haruhi/Kyouya is apparently more popular than Haruhi/Hikaru.
Tamaki/Kyouya is also a popular ship, particularly among those who pair Haruhi with someone else.
Kanzaki Kaori is also a more popular pairing with the main character (Touma) than the titular character.
Fans of Cowboy Bebop can't agree on who Spike should be with, but they do seem to agree that it's not his canon love interest, Julia. It helps that Word Of God has confirmed Spike and Faye had a thing for each other, but Spike's obsession with his past prevented him from doing anything about it.
Mahou Sensei Negima! began with the daunting task of giving the male lead an entire classroom of love interests, a whopping thirty-one girls, with more added as time went on. Eventually six women emerged as having the best chances of hooking up with Negi, and fandom was pretty evenly split among them. Then the series ended. Badly. Very, very badly. And ambiguously, with a "Where Are They Now?" Epilogue that covered everyone's lives except on this one issue; it did rule out six characters, but none of them were the main six. The final chapter ended with Negi saying he might like someone, but he's ten-years-old, it's not really a sign of a final commitment.
Each of Ash's female companionsnote not countingBonnie have had their share of Ship Tease moments, and, thus, their share of supporters for his hand, mainly correlating to either when the fan first entered or which season was a fan's favorite. As of the end of Best Wishes, however, Mistyhad stood the test of time; though she was aided by external support during her tenurenote specifically, a minor Writer Revolt in Japan sneaking in the Ship Tease compounded by Dub Text in the translations, plus an added Love Song in the 2 B A Master CD,, other pairingsnote some being FPCs in their own right, see below, and, in Iris' case, characterization issues[[/note]].
Ash's Mom (Delia)/Professor Oak had a strong following for a while, partly due to Oak acting as Ash's father figure most of the series, and partly due to their offscreen (and several onscreen) locations being in close proximity.
Though Dawn and Paul hate each other and don't share any Ship Tease moment together, somehow, this pairing has a lot of followers.note One of the reasons this ship is so popular is because of that one scene before Ash and Paul's battle at the Sinnoh League, where not only does Paul actually open up to Dawn, but also has Dawn blush at one point.
In the Pokémon Special manga it tends to be Red and Yellow. Some go for Red and Bluenote Green in America. Bluenote Green in America/Silver, Gold/Crystal, and Ruby/Sapphire teeter on the edge of canon, but can still be called this. With any other manga? Most fans don't know of any other manga. A slight example is Pokémon: Diamond and Pearl Adventure, where Jun and Mitsumi seems popular. Cynthia and Mitsumi have a small following as well.
Contrary to the games, Black/White is a much more popular ship amongst Pokémon Special fans then N/White, whose game counterparts are the components of one of the most popular game ships in existence. Ironically, the one thing that had Special fans dropping the N/White like hot potatoes was the one thing that made their game counterparts so popular. Can you say, FerrisWheel?
Magical Girl Lyrical Nanoha is infamous for its Ship Tease — sometimes metric tons of it — for couples that are not official at all. And that means basically all potential pairings, since there's exactly one Official Couple in canon to date... an off-screen hookup between a member of the supporting cast and a glorified extra. The fans have responded with Fan Preferred Pairings for most of the main cast, particularly Nanoha/Fate, Suzuka/Arisa, Hayate/Vita, Subaru/Teana, Caro/Erio/Lutecia, and Vivio/Einheart. (That is, not counting the harem theory.)
Many fans think that Saeko would be a better match for Takashi than Rei. Likely because of her unbridled Ax-Crazybadassery and because she's pretty hot. Though a fair amount of the pairing's popularity is also due to shippers simply not liking Rei.
Saya and Hirano have a respectable fanbase as well, thanks to the manga giving the ample amounts of Ship Tease. Such as this scene from chapter 29.
One Piece has a few, despite No Hugging, No Kissing being heavily hinted at as the author's intent. The fandom heavily prefers pairing Luffy with Nami, citing a unique relationship between the two as evidence, as well as the fact that author Oda's wife apparently cosplays as her. On the Yaoi side, Luffy is often paired with Zoro, or Zoro with Sanji. Other fan-favored pairings include the sorta-obvious Usopp and Kaya, as well as Zoro and Robin.
A more extensive list includes:
Franky/Robin (due to them having been described as the "dad" and "mom" of the Straw Hat crew, numerous scenes of Character Development they share; especially their recent Punk Hazard moments, and both being strongly connected to the Myth Arc.)
Sanji/Nami or Sanji/Robin (his constant canonical swooning over both of them plays a role)
Zoro/Nami (due to their Vitriolic Best Buds nature; fan artwork has even been dedicated to this one)
Zoro/Sanji (The whole rivalry between the two strongest and the fact that Filler has the two almost kissing...twice)
Chopper/Robin (largely because of a filler episode post-Alabasta that centered on his initial interaction with her, despite the implied bestiality)
Nami/Kalifa (because of how the anime portrayed their fight at Enies Lobby)
Usopp/Perona (For those those two being way too alike, and the fact Usopp has been the only man to tame her bossy personality)
Usopp/Kaya (Childhood Friends)
Smoker/Tashigi or, to a lesser extent, Smoker/Hina (canonically he has a good working relationship with both of them, and Hina has a good understanding of Smoker's personality from their days at the Marine academy)
...yeah, the possibilities are endless.
Some fans of Tears to Tiara like to pair Arthur and Octavia together, since they're both noble warriors and swordsmen with Sad Pasts that involve their dead loved ones. And of course the fans were excited when they saw episode 10.
The favorite pairing among fans (And the creator, believe it or not) of Infinite Stratos seems to be Ichika and Charlotte Dunios. It seems to help that Char is the only non Tsundere member of the harem.
Due to how incredibly Adorkable Laura is after her defrosting, many fans add her into the Ichika/Char pairing as an OT 3.
Rein and Eclipse from Fushigiboshino Futago Hime were more popular (in fact, the most popular pairing) in Japan than the Official Couple Fine and Eclipse, at least, before the second installment began. Even Mayuki Anan, the artist of the manga adaptation, seemed to prefer them, as Rein and Eclipse got more Ship Tease than any other pairing.
While the slash fans dominate the fandom, L/Misa fans contribute their share of fan art as well.
From Yu-Gi-Oh!, Yugi/Yami Yugi, Jounouchi/Kaiba, and just about every combination of Bakura, Marik, Dark Bakura and/or Dark Marik. On the hetero side, Yami Yugi/Dark Magician Girl (or Atem/Mana), Shizuka/Kaiba, Isis/Kaiba, Mai/Yugi, and among others.
Puppyshipping (Jounouchi/Kaiba) is probably the biggest pairing in the whole fandom, despite the fact that the two are neither even remotely friendly nor actual rivals, treating each other with a fairly dismissive hatred. It mostly comes from that one time with the dog suit (which wasn't even in the manga).
From Yu-Gi-Oh! GX, Juudai/Asuka (Jaden/Alexis in America) or Juudai/Johan (Jaden/Jesse)note The fandom is quite neatly split in two, with one half shipping the former, and the other half shipping the latter. As for what the Official Couple is... let's just say Juudai goes both ways... sort of.
Yu-Gi-Oh! 5Ds has the unusual case of Jack and Carly, where the pairing was an Official Couple... until Carly got Laser-Guided Amnesia and more or less demoted to a member of Jack's harem (which he decides to dismiss at the end of the series). The number of fics of the two quickly hooking back up is staggering.
Ushio/Mikage is another one. For a brief while, it seemed like Ushio had an unreciprocated crush on Mikage, but this fizzled out when Mikage also became part of the Jack harem. The two of them have become an incredibly popular Beta Couple in Jack/Carly fics.
Shizuku and Natsuru in Kämpfer are essentially this in the eyes of the fans, who love seeing Shizuku trolling the hell out of Natsuru. The official according to the Light Novel is Natsuru and Akane, while the anime opted for the "everyone wins" route.
Within the Kashimashi: Girl Meets Girl fandom it's extremely rare to see someone who ships Hazumu and Yasuna. This is despite, or maybe because, she was the girl Hazumu was going after for most of the series. The shipping was so noticeable that an anime OVA came out that killed the Hazumu/Yasuna ship with a flimsy excuse, to get Hazumu and Tomaritogether. It has a mild excuse in the anime, where the ending before the OVA does have aspects of Ass Pull.
It's also worth noting that the manga did have Hazumu end up with Tomari at the end. The anime came out before the manga ended, though, so it's possible that the manga's ending was influenced to some extent by the popularity of Hazumu/Tomari.
In Tsubasa Reservoir Chronicle Kurogane and Fai are the biggest non canon pairing due to the massive amounts of Ho Yay between them, and the fact that neither of them have any love interests. Some fans are desperately looking for Kurogane/Tomoyo hints though, which makes everyone else laugh sardonically because...well, everyone who is familiar with the Tomoyo of Cardcaptor Sakura knows why. Word Of God has (admittedly rather begrudgingly) moved them up to a more official status.
Tsubasa's Sister series xxxHOLiC has the similar dynamic duo of Doumeki and Watanuki as the, without a doubt, most popular pairing in the fandom. It is very rare to find anyone who ships Watanuki with anyone other than Doumeki, despite the fact Watanuki 1) never fully gets over his unreasonable distaste for Doumeki, 2) has a massive crush on his classmate Himawari and 3) by the end, has at least three other potential love interests.
Fruits Basket is a shipping goldmine! While many support the canical Kyo/Tohru, Yuki/Tohru and Kyo/Kagura complete the love triangle with a large fan base. On the yaoi side, Yuki/Kyo and Yuki/Hatsuharu are pretty popular too.
Vampire Knight has Zero/Yuuki. Many fans also support the relationship between minor characters Senri and Rima.
Fairy Tail has its fair share. A good majority of the fandom ships Natsu/Lucy. Jellal/Erza and Gray/Juvia is also abundantly supported, helped in fact by the continuous Ship Tease for the former and the adorableinteractions for the latter. Beta Couple Gajeel/Levy is also unanimously supported by the fandom. Cobra and CubeliousKinana are also very popular. Evergreen and Elfman are basically canon now, to everyone's amusement but their own.
In the Hayate the Combat Butler fandom the majority of fans seem to be divided between Hayate/Hinagiku and Hayate/Athena. While Hinagiku continues to completely overshadow the entire cast in terms of popularity, Athena is a firm second and discussions on the forums can be split pretty evenly. Notably neither of the girls is one of the main heroines, those being Nagi and Maria who have more supporters than the other 'auxiliary' pairings but not nearly enough to compete for fan-favor.
Wataru/Saki is also incredibly popular among the fandom despite Wataru being interested in Isumi and Sonia having an obvious interest in him. Recently in the manga it seems that the Wataru/Saki shippers might have won after all, as Wataru confessed to Isumi that he loved her and has since dropped out of Hakuou to focus on his business with Saki.
Card Captor Sakura has Eriol/Tomoyo, even though Eriol/Kaho is canon, and Tomoyo is in love with Sakura. But many fans will pair them because of their similar personality traits and that they find Eriol dating Kaho to be "creepy" because of their apparent age-difference (Word Of God has stated though that Eriol is Fujitaka's age, technically making him older than Kaho and way older than Tomoyo).
Many fans of Midori no Hibi seem to prefer Ayase/Seiji more than the official couple.
K-On! has Ritsu/Mio, and also Yui/Azusa, even though recent chapters of the manga seem to be Ship Teasing Yui/Akira and Ui/Azusa. And then there's Sawako/Mugi. The Fan Preferred Couple among the background characters is Akane/Eri.
In the Binbogami Ga fandom, the Pixiv fanartists are very much in favor of Ichiko and Momiji.
Tsukushi was originally supposed to end up with Rui in Hana Yori Dango but Tsukasa/Tsukushi became so popular with fans it became the Official Couple, which is ironic because after the manga finished, Rui/Tsukushi became the Fan-Preferred Couple because a lot of people thought Tsukasa became an incredible jerkass at times who kept upsetting Tsukushi while Rui gradually became a much more friendly and warm young man who was always there for Tsukushi.
Mizore/Kurumu ever since their on screen kiss. Tsukune/Inner Moka is also the most popular pairing of the Harem.
Some Sekai-ichi Hatsukoi fans would prefer Chiaki with Yanase than Hatori. This has to do with Hatori brutally raping Chiaki and episode 16 that pulled everyone's heartstrings.
Medaka Box has Zenkichi/Emukae. Medaka/Kumagawa definitely seem to be fairly popular as well, compared to the canonical affection Zenkichi has for Medaka which seems to be reciprocated as of Chapter 140.
Gintama has so far no Official Couples, and the chances of there being any are slim, but this has not daunted the shippers in any way. Okita/Kagura, due to the Foe Yay and Belligerent Sexual Tension between them, are ardently shipped together. A close second would be Gintoki/Tsukuyo, especially after the Ship Teasy Red Spider arc. Yaoi couples such as Gintoki/Hijikata and Hijikata/Okita are also hugely popular due to a large part of the fanbase consisting of Yaoi Fangirls.
Despite the fact that they're half-siblings, Serpico/Farnese is still a popular pairing within the Berserk fandom. Even though she's arranged to marry Roderick, there's not much approval for that pairing in the Berserk fandom. Despite a strong Guts / Schierke contingent and Guts' status as the Fandom Bicycle, the Official Couple of Guts / Casca is still Fan Preferred due to their mutual Woobiehood and the tragic, doomed nature of it all.
NaoandReika, who are childhood friends, are already proving to be quite a popular couple as well, and have several hints scattered around. The "Nissan combo", Nao and Akane, just about rival them in popularity.
Also, Joker and Reika, despite the fact that the two times they've actually interacted, in episode 23 and 43, they were fighting against each other, with Joker being as creepy as he always was.
While the official pairing in Guilty Crown is quite obviously Shu and Inori, many fans actually consider Ayase or Hare as better romantic partners.
In the Nightwalker fandom, there are those who would ship Shido with either Yayoi or Cain.
Popular Hyouka fan pairings include Oreki/Irisu, Oreki/Mayaka, and Eru/Irisu.
Many Ayashi no Ceres fans consider Yuuhi to be a better match for Aya than Tooya, though she actually does sort of end up with him. Not on-screen, but considering Tooya is dying already...
Episode 13 of Dog Days gives Cinque/Millhi as the Official Couple, but there's a lot of fanart out there for Cinque/Eclair.
There is little to no romance in Yotsuba&! but Koiwai/Fuuka is easily the fan favorite. Rule 34 is generally frown upon when it comes to this series but they obviously exist, and probably 90% of them are on these two. It helps that any ship tease that exist in the manga at all are between these two.
While the canon Keith/Allura pairing has a LOT of fans, an almost equal number of Voltron fans like to pair Allura with Lotor, in part because of Lotor's Draco in Leather Pants vibes, and in part of scrub off some of the Purity Sue aspects of Allura. It should also be noted that a small but vocal minority would prefer Lance be with Allura.
A strong portion of the (Japanese) Seiyuu Ka fanbase ships Haruka/Hime while lesser portions ship Senri/Hime and Mizuki/Hime.
If the forums of various sites are to be believed, then Akira/Rion is by far the most popular pairing in Cage of Eden, and for good reason, due to their willingness to protect and take care of each other, no matter what happens. Akira/Mami seems to be gaining popularity quickly, though.
It seems that a lot of Aquarion Evol fans, at least in the U.S., preferred Amata to be with Zessica and Mikono to be with Kagura.
In The Cat Returns, Haru/Baron is one of the most impossible couples to actually get together (except through very powerful magic, more so than the Cat Kingdom's cat turning abilities), with Baron being a foot-high, half cat living statue and Haru being a fully human, normal height school girl. Doesn't stop the fans from shipping them.
Jack/Snow is surprisingly more popular than Jack/Pano (if only because of the Ghost Chess arc) on forum discussions.
On the Ho Yay/Foe Yay side, you have Ginta/Alviss, Phantom/Alviss and Rolan/Alviss with the first two being nearly tied.
Basically, disregarding O Cs and self-inserts, the most popular ships seem to be Ginta X Alviss, Ginta X Phantom, Alviss X Phantom, or some combination thereof, though some might argue the Yaoi fans are an extremely vocal minority. As far as heterosexual pairings go, Ginta is almost exclusively shipped with Snow, and Dorothy is near-universally paired with Nanashi. Jack is either left alone or paired with Pano, or rare cases with Snow. Alviss is... Unsurprisingly almost never paired heterosexually, but in the rare instance he is, it's usually Belle.
Surprisingly, even with all those ship tease between Ako and Shou, the most popular ship of Thriller Restaurant is Anko/the Garçon. It must has something to do with the ED and the implication that they really have met before.
More preference has slowly shifted toward Shu now, though. At least for fans who read the manga. Since only in the manga did Shu discover that "Before" and "After" Tsukimi are the same person. His conclusion? He doesn't care, still loves her, and is willing to even go along with her Jellyfish obsession.
While Ken and Jun officially got together at the end of the third series of Science Ninja Team Gatchaman -Gatchaman Fighter-, there is part of the fanbase that prefers that Jun be with Joe instead, feeling that Joe is more interesting of a love interest and pointing to various moments in Gatchaman II where the two seemed closer than Ken and Jun had. This extends to the only (at time) English adaptation of the same sequel, where the dub writers seemed to be pushing Joe and "Kelly" more as a possible couple.
With the exception of the rare Sakurako/Akari ship, the Yuru-Yuri fandom does not ship Sakurako or Himawari with anyone but each other.
For Strike Witches fans as of late, it's been Perrine and Lucchini. Many of their interactions are rather amusing in terms that they're complete polar opposites,with Lucchini almost always teasing her, especially episode 10 of the second season, where they share tons of Ship Tease moments, including Lucchini hugging Perrine as she's scared, then later throwing a sword to Perrine to defeat a golem, which got fans curious on how well they work together.
In Date A Live, while Tohka is the lead girl, fans would prefer shipping Shido with Kurumi since they snark so well with each other.
Though nothing in the Puella Magi Madoka Magica fandom beats the Official Couple double-bill of Madoka/Homura and Kyouko/Sayaka, Kyouko/Mami comes the closest, and more or less outstrips fans of Mami's usual mate in merchandise, Nagisa. Part of it's that Kyouko/Mami is more entrenched and Mami/Nagisa is comparatively young, part of it's that Nagisa, being the Token Mini-Moe, produces some fairly self-explanatory squeamishness when paired with resident Ms. Fanservice, part of it's that Mami's relationship with Nagisa doesn't seem as romantic as with Kyouko... either way, it's the only case where a pairing endorsed by a spinoff beats a pairing endorsed by a feature film.