Mako/Korra was this in regards to Mako/Asami, but when Mako/Korra became canon, Bolin/Korra and Iroh/Asami had a huge rise in Fan-Preferred Couple status, mainly due to Mako's (and to a lesser extent Korra's) Base Breaker actions, especially in the second season.
As of the thread season, Korra/Asami has grown hugely in popularity with the two spending nearly all their time together, from little things such as eating together at big dinners, Asami teaching Korra how to drive to big things like Asami staying by Korra's side while she is wheelchair bound after her battle with Zaheer in the finale. Asami even holds Korra's hand and tells her that she while be there for her should she need to talk.
Within hours of their debut episode, Avatar Wan and Raava started getting shipped by a surprising number of fans. Helped along when one fan drew a humanized version of Raava that the newly christened ship's shippers immediately latched onto.
Craig and Tweek; they are the second most popular pairing (after Stan and Kyle) which is especially surprising considering that they only openly interacted in in one episode. (Where they were manipulated into beating the crap out of each other. Tweek was shown in a nonspeaking cameo as a member of Craig's gang in a later episode, but most use the fight as the primary basis.)
Much of the fandom dislikes Daria/Tom and would have preferred that Daria's one-sided crush on Trent eventually been noticed and requited.
To say nothing of the Daria/Jane shippers, who started from day one and are still going strong.
For some bizarre reason Jane also gets paired up with Mr. D of all people fairly often.
Meanwhile, fics taking place before Daria moved to Maryland often pair her with Earl, a gun-toting JD based on her strangely breezy attempt to exchange banter with him in the middle of a gunfight in the episode "Incognito".
Beast Boy/Raven shippers. The creators of the show repeatedly stated that Beast Boy/Raven would never happen, yet it was an increasingly popular and a preferred complementary ship for Starfire/Robin shippers. At the very least a substantially large amount of people preferred it to the official canon couple of Beast Boy and Terra (the difference on FF.net is about twelvefold in the romance category).
Cyborg is most commonly shipped with Bumblebee despite that in the Recursive Adaptation, Teen Titans Go!, both Bumblebee and Cyborg have suitors. The ironic thing is, the creators didn't want Cyborg and Bumblebee to seem like a case of Pair the Spares, so they made the two characters initially really dislike each other to go against this, but the Belligerent Sexual Tension that resulted is one of the reasons the pairing is so popular.
Cyborg is also often paired with Jinx (indeed all three of them doesn't seem that uncommon). The pairing search shows that to be more popular than Cy/Bee (it should be noted that Cy/Jinx is far from catching up with Kid Flash/Jinx), but it's difficult to judge since Cyborg is usually in a secondary pairing.
In the Batman Beyond fandom, the majority of the fans go for Terry with his best friend Max or one-time girlfriend Melanie. Few actually pair him with his canon girlfriend Dana Tan, as she's the least developed character of the three. In the Season One DVD Behind the Scenes featurette, it is discovered that Alan Burnett wanted to write an episode where Terry and Max ended up together, but Bruce Timm refused, as he'd originally intended the episode to have Terry and Dana stay together, and Terry ends up getting hitched to Dana in the future as shown in the JLU episode "Epilogue."
Brian/Stewie from Family Guy gets a lot of love, given how blatant Stewie's affection for Brian is and the amount of episodes centered around the two and their interactions. The episode Brian and Stewie is especially well-received by fans of Brewie. The couple gets tons of fanart and fanfiction, some of which can be, erhem, erotica.
The Simpsons has fans that are not as shipping-oriented as some other shows, but there are several of these. For example, Lisa/Nelson is vastly preferred to the edging-towards canon Lisa/Milhouse, presumably due to Milhouse being an annoying Stalker with a Crush.
Super Robot Monkey Team Hyperforce Go! has a weird case of this. Hints dropped in the series originally seemed to show Otto/Nova as canon, but it seemed like almost everybody in the fandom shipped Sprx/Nova. Then hints of that started to show and eventually it became the canon. A comment from one of the voice actors mixed with that the creator does pay attention to the fandom seems to hint that the coupling was changed because of this, making the FPC the Official Couple. Ironically, though Sprx/Nova is still the main fandom ship, there are now more Otto/Nova shippers around filling the FPC bill.
Professor Utonium and Ms. Keane has a strong fan following. They were the subject of one episode late into the series, and it was thoroughly deconstructed and eventually annulled by Ms. Keane's cat, with the Professor having an aversion to cats due to one being the Big Bad of an earlier episode.
Chip/Gadget in Chip 'n Dale Rescue Rangers, to the point where Portmanteau Couple Names aren't necessary anymore because the only terms needed are "pro" (for being in favor of Chip/Gadget) and "anti" (for explicitly opposing this ship, regardless of alternatives). Well, okay, and Dale/Foxglove.
On Tiny Toon Adventures, Fifi la Fume's occasional official love interest is Hamton J. Pig, mostly because of Pair the Spares. However, a quick search on Deviant ART reveals that a sizable portion of the fandom prefers to ship Fifi with either of her one-time romantic chase victims, Calamity Coyote or Furrball Cat, the latter likely due to her predecessor Pepe le Pew being officially paired with Penelope Pussycat.
There are no pairings in The Zeta Project, but fandom loves Zeta and Ro together as a pairing. It's actually a challenge to find fanfics that aren't Zeta/Ro.
Early production, according to the writing staff, would have involved developing Bennett and Lee as having romantic feelings towards each other, in order to make her actions in what ended up being Season Two more poignant. This was scrapped because Executive Meddling wouldn't allow a married man to have even an emotional affair on children's television. Despite leaving as much of their friendship intact as possible, however, none of the fans went for Bennett/Lee as a ship, and instead set sail the good ship West/Lee.
Number 1 (Nigel)/Number 5 (Abby) are a significantly more popular ship than the canonic Number 2 (Hoagie)/Number 5 and seems to be on the same level of popularity as the canon Wally/Kuki.
Before the increasing Ship Tease in later seasons solidified Wally/Kuki as an Official Couple, they were this in the first season as well, with only one Day in the Limelight episode with each other that could remotely be considered shippy. This episode, "Operation OFFICE," is widely hailed by their shippers as the episode that got them interested in the ship in the first place.
Numbah 1/Numbah 362 (Rachel McKenzie) is another popular pairing. Many assumed this 'ship would sail after Nigel and Lizzie's break-up in the final season, but Nigel's promotion to the Galactic Kids Next Door sunk it instead, still, that hasn't stopped many fanfic authors sending Rachel off into the stars in pursuit of him...
Although Fillmore! was created as a No Hugging, No Kissing series, Fillmore/Ingrid have a fanbase of a rather impressive size. The shippers have a lot to base off of, since their buddy-cop conversations can often be taken as a subtle Double Entendre, sounding somewhat flirtatiously on more than one occasion.
Even though Rocket Power was mostly No Hugging, No Kissing, there's a large following for Twister/Reggie. It's the most commonly encountered pairing in Rocket power fanfiction.
Although the show often dabbles in Ho Yay and Ship Tease, The Penguins of Madagascar doesn't really have any canon pairings that last. However, Skipper/Marlene is by far the most common pairing among fans, which time and again proves unsinkable.
Sym-Bionic Titan: The pairing of Ilana and Lance (dubbed Ilanca by the shippers) has been favored since the very first episode, despite how in the show they're posing as siblings and have other potential love interests, and the show's creator Genndy Tartakovsky, has stated in interviews that he wants their relationship to be a platonic one.
Ahsoka/Rex (Rexsoka) remains the most popular Ahsoka pairing, even though she has a canon love interest in Lux Bonteri. This is probably because Lux is comparatively new on the scene, and Rexsoka was already well-established in the fandom before his episode premiered in Season 3. Karen Traviss and Karen Miller's teases towards Rexsoka in the novels did not help things.
In general, clone/Jedi ships are greatly preferred to canon ships. Aayla Secura and Commander Bly are one example, but that ship was widely supported before the show even started thanks to the characters' interactions in the comics. Barriss Offee/Commander Cody, however, is largely unique to The Clone Wars fandom. The two often star as a Beta Couple in Rexsoka fics, even though Barriss and Cody never interacted in cartoon or comics.
While the vast majority of the cast is shipped with pretty much everyone else, Lyra and Bon Bon tend to be paired almost exclusively which each other. Case in point, do a search for either character and you'll get almost nothing but Lyra/Bon Bon pictures, whereas if you try a similar search with any other characters you'll probably get five or six different pairings before you get past the first page. There are outliers that pair them up with other characters, of course, but the pairing is so widespread in the fandom that in most fanworks its assumed to be the case unless it's explicitly stated otherwise.
Vinyl Scratch(DJ-Pon3)/Octavia shipping is also extremely popular, with both of them being fan favorite musicians.
Derpy Hooves and Dr. Hooves are very popular together, to the point of the Doctor being considered the father of Derpy's fanon daughter Dinky.
By far the most popular pairing is Knock Out/Breakdown, despite Breakdown having shown interest in Airachnid.
Jack/Arcee is quite popular as well, even though Word of God denies any romantic feelings between them. But due to the Relationship Writing Fumble, it gets hinted alot that there may be some deeper feelings between them, which only gives the fans more fuel.
G1Prowl and Jazz might well embody this. In canon, they barely interacted and when they do, they (usually) hate each other. Last count on FFN for Jazz/Prowl fics? 411.
The episode "What Was Missing" caused an explosion in the popularity of Bubblegum/Marceline, and from there it grew until it almost dominated the whole fandom, with the largest chunk of fanart and fanfiction devoted to them.
As of the "Incendium"/"Hot To The Touch" two-parter, Finn/Princess Bubblegum became this for those who still shipped it, with Finn shifting to a Star-Crossed Lovers scenario with Flame Princess.
Meanwhile, in the Gender Flipped "Fionna and Cake" world, Fionna has a crush on Prince Gumball, but most fans like to ship her with Marshall Lee, especially after "Bad Little Boy". Gumball with Marshall Lee are predictably popular as well, given they're counterparts of Bubblegum and Marceline mentioned above.
There are also quite a few who ship Fionna with her template, Finn, since they are both human. Fionna is a fanfiction character in Finn's world, but this hasn't stopped fanfic writers from finding some way to have the two meet, from dimensional portals and other forms of magic, to Fionna living on a separate continent/country called the Land of Aaa.
While the Kevin/Edd pairing always had a fanbase, in spring 2013 it became extremely popular.
Edd/Eddy and Edd/Marie used to be the most popular ships, but lost popularity in favour of Kevedd. They still have their fans though, especially Edd/Eddy, as most Edd fans ship him with both Eddy and Kevin.
A good amount of people, particularly the ones who prefer May Kanker over her sister Marie, seem to love Edd/May (noticing the pattern?), also thanks to their Ship Tease in the Valentines' Day special.
El Tigre has El Tigre and Black Cuervo. It was so popular 'Tigre + Cuervo Forever', a catch phrase for the ET/BC following, became the title of an episode. Meanwhile, Frida gets paired with either Dr. Chipotle Jr or Sergio a lot. Frida/Django is quite popular, too.
In Sidekick Eric has a crush on Vana, but fans like him better with Mandy or Kitty instead.
The Critic has Jay and Alice, which is one of the reasons why the web series wasn't well received. Considering how much trouble Jay went through in season 2 to be with Alice (especially the next to last ep), you can't blame their reaction at seeing Jay trying to woo another girl.
Happy Tree Friends has Flippy and Flaky as a favorite pairing. This is despite all the times Fliqpy has killed Flaky, and Flaky even stabbed Flippy once. Hell, people aren't even certain what gender Flaky is, but it looks like ever since "Without A Hitch" the writers have given in to fanon.
Since the beginning, many fans have embraced the idea of Warden/Mistress (Misden or Wardess) getting together, most of the time being aware that they are foes. As of Season 3, this does not appear possible.
Although the same season 3 premiere also created a faction of Alice/Mistress shippers, even though the relationship would in likelihood be as one-sided as Warden's affections for Alice (as Alice seemed unimpressed at Mistress' change and remarked on forgetting how "needy" women can be).
Despite their rather limited interaction, Dipper and Candy have quite a bit of fanart.
Although the show is told from Dipper's perspective which wants you to root for Dipper/Wendy, most fans go for Robbie/Wendy. This pairing was canon for a bit of the series, but as of episode 17 it is unclear whether the two will get back together.
There's a sizable fan community for Nick/Mina, who ship them because Nick is one of the nicest characters in the show and Mina is a long-suffering woobie.
That said, pretty much everyone ships Laney and Corey, with the vast majority of fan art featuring them.
The Hefty/Smurfette fan shipping in The Smurfs even went so far as to have an episode "Hefty's Wheelsmurfer" be named "Fortachon y Pitufina" in the Spanish dub, despite the episode having nothing to do with Hefty and Smurfette in any fashion of a relationship together.
So far there is no Love Interest for anyone in Wander over Yonder, but Wander/Lord Hater is already being hardcore shipped. Wander/Sylvia is gaining popularity, too.
In X-Men: Evolution, Scott/Rogue were shipped hard. Even though the two have no particular relationship in the comics, the cartoon explored their similarities in greater detail: both have involuntary powers, both come from unstable families and were adopted by Xavier, and both are socially awkward with Scott being a nerd and Rogue a goth. In the handful of episodes where they bonded (the Christmas Episode in particular), most fans felt Scott had better chemistry with her than his canon love interest, Jean.
In Arthur, some fans prefer Arthur/Sue Ellen as a couple as opposed to the implied Official Couple of Arthur/Francine. Some fanfics even pair up Arthur with Sue Ellen.