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.
Another fan preferred couple would be the genderbent versions of Marceline and Bubblegum, Marshall Lee/Gumball.
Finn is often paired with his genderbent counterpart, Fionna. Though just as many authors and artists depict them as either Just Friends or long-lost twins, usually the latter.
Fionna and Marshall Lee already had plenty of support even without him saying or doing anything. But then"Bad Little Boy" rocketed the ship to the top tier and it hasn't looked back.
Tommy/Kimi and Chuckie/Angelica are both fairly popular in the All Grown Up! fandom, the former because it is suggested that she might have a crush on him in one episode and the latter because of the surprising amount of chemistry they have as an Odd Couple.
The Amazing World of Gumball Among the show's fandom, Gumball and Carrie ship remains popular even Gumball and his love interest, Penny, become official couple in S3. Interestingly, Ben, the creator of the show, finds the fans' pairing amusing.
Despite Sokka having a canon girlfriend in Suki, more people ship him with Toph (who canonically has a Precocious Crush on him).
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."
In Ben 10 the preferred couple was definitely Ben and his cousin Gwen.
Ben 10: Alien Force, According to FF.net, four of five most favourited romance stories are Ben/Kevin.
Ben 10: Omniverse introduced several possible love interests for Ben before settling with Kai. Unfortunately for Kai, she had two things going against her: 1) the shipping was heavily focused in the final arc, and the writers introduced Spanner to actively force the pairing, and 2) Looma Redwind and Esther were very popular since their debut. Esther/Ben itself is the more popular het ship for Ben.
Until well into 1990, Chip 'n Dale Rescue Rangers' preferred shipping was Dale/Gadget, pairing the only girl on the team with the fun-loving goofball rather than with the bossy workaholic. But then came "Good Times, Bat Times" and brought Foxglove with it. She and Dale looked so cute together in what came closest to a happy relationship for a Ranger in the entire show that Dale was out of the Love Triangle for many many Rangerphiles. Fan Fic and Fan Art keep shipping the two, and the Boom! Comics support this ship as closely to Canon as possible.
This did make way for Chip/Gadget, but while they do have a whole lot of supporters, they're the reason for a case of Broken Base: Despite Tammy's crush on Chip ("Adventures in Squirrelsitting") and Gadget's potential crush on Sparky ("Does Pavlov Ring a Bell?"), the question isn't with whom to ship Chip and/or Gadget. It's rather whether or not to ship Chip and Gadget. Among the fans, there are the Pros who support this ship and make it the second Fan-Preferred Couple, there are the Antis who oppose it, whether or not they have an alternative, and then there are the Neutrals who keep themselves outside of the debate.
Codename: Kids Next Door: Just about any non-canonical pairing involving Nigel Uno is more popular than his canon relationship with Lizzie — though the most popular seems to be Nigel/Rachel (1/362), with Nigel/Abigail (1/5) as the second most popular.
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.
In Danny Phantom, the main shipping of Danny and Sam Manson is quite polarizing. Almost all of the criticism is directed at Sam, for her hypocritical morals, all of the Character Shilling she gets, the panned third season kept teasing their attraction to each other and the Alternate Character Interpretation that Sam is in love with Danny Phantom, not Danny Fenton, as she fell for a boy who resembled Danny's ghost form and was angry with him for giving up his powers. As such, Danny is often shipped with other characters, with the most notable being Valerie Gray and Ember McLain.
Much of the fandom dislikes Daria/Tom and would have preferred that Daria's one-sided crush on Trent eventually been noticed and requited.
For some bizarre reason Jane also gets paired up with Mr. D of all people fairly often.
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.
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.
Meg/Neil for some. In "8 Simple Rules of Buying My Teenage Daughter" and "Once Bitten", she was actually happy to go out with 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.
One of the most popular ships in the fandom, despite their age differences, is Dipper and Wendy (Wendip for short) given their incredible chemistry.
The other popular ship in the fandom happens to be Dipper/Pacifica (Dipcifica for short). Heavily teased by the creators during "Northwest Mansion Mystery" and made canon (on Dipper's side at least) in a post-series book.
Alternative circles of fans, like on the Archive of Our Own, have Dipper/Bill as one of the most popular couples.
Mabel/Pacifica (Mabifica) is very popular due to people liking how their personalities would work together. There's a good chunk of Ship-to-Ship Combat between it and Dipcifica fans, though a Sibling Triangle is avoided in most fanworks.
Grojband, 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, everyone ships Laney and Corey, with the vast majority of fan art featuring them.
Invader Zim is a No Hugging, No Kissing show, but still has several common pairings. The most popular (but also most reviled) is the perceived Foe Yay between Zim and his rival, Dib. For a straight example, Zim and Gaz (Dib's malevolent little sister) is also extremely popular, with Dib and Tak (a one-episode wonder female Irken invader) being less popular than either of the aforementioned, but still a major presence in the fandom.
The series launched with a strong following from Korra, the main character, and Mako, as opposed to the starting couple of Mako/Asami.
Korra/Asami was a small but popular crack ship alternative to Mako/Korra and Korra/Asami during book 1. Later on in the series, a good amount of the fandom eventually gravitated towards Korrasami due to Makorra and Masami both failing and the chemistry going on between the girls. At the end, Korrasami became the Official Couple.
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.
There are far more fanworks involving Lin and Tenzin than there are of Tenzin and his wife Pema. Tenzin is Happily Married with four kids, but a comment in an early episode caused fans to lean towards Linzin. In their youth Lin and Tenzin dated but broke up. Pema had a little to do with it, however the two were too different to work out anyway and had been growing apart even before Pema came into the picture. A large portion of Tenzin-centric works focus on his past with Lin, are outright AUs where they don't split, or have Tenzin cheat on Pema with Lin. Pema even gets hits by Die for Our Ship and is sometimes depicted as a home wrecker.
The Lion Guard fandom can't seem to make heads or tails on who to even ship Kion with. He has no less than 5 times the number of options for significant others than any other protagonist in the whole franchise has, so nearly everyone has a different preference.
Kion and Fuli is a fairly popular ship, but it's often criticized for being an interspecies pairing. The select few who give them biological offspring typically get it worse than most.
Seeing as Jasiri has come the closest to outright with flirting with Kion so far, shipping the two was a given from the start. Though, considering she is a hyena...
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. The episode "Slice of Life" has the Doctor has the one pony Derpy turns to and one of the few ponies that does not view her as a walking disaster (the Doctor even let's Derpy walk around his "workshop" and play around without a care) and towards the end Derpy gives the Doctor a sweet hug. Let this ship sail!
While the vast majority of the cast is shipped with 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. When the two met up at a Ponyville market in Putting Your Hoof Down, their saddle bags had each other's cutie mark on them And thensent over the top by their human versions' "love duet" performance in My Little Pony: Equestria Girls – Rainbow Rocks. While "Slice of Life" had them constantly refer to themselves as 'best friends', their constantly looking at each other with bedroom eyes and having blatantly romantic body language has many in the fandom convinced that not only has their ship sailed it is on an around-the-world journey.
Vinyl Scratch(DJ-Pon3)/Octavia shipping is also extremely popular, with both of them being fan favorite musicians. The episode "Slice of Life" even canonized that the two are roommates.
The introduction of the dragon princess Ember in Season 6 has seen a landslide of stories and art pairing her with Spike.
While pretty much every main character is a Launcher of a Thousand Ships and the main characters are paired in every combination, the most popular ships seem to be Dash/Pinkie, Dash/Applejack, Dash/Fluttershy, and Rarity/Applejack. These are in large part due to their chemistry and to their screentime together, especially in early episodes.
Phantom Investigators was for the most part pretty No Hugging, No Kissing among the four leads, with any romance with them only being crushes on one-shot or background characters that did not go past one episode. While the show doesn't have a large fanbase due to it's obscurity, many diehard fans of the show tend to ship Daemona and Casey. Doesn't hurt that many of their interactions could easily be read as Ship Tease, such as Daemona wrapping her arm around him at one point in "Birthday Presence" and calling him adorable at the beginning of "Were-Dog".
Ferb and Gretchen has become popular with those who have a hard time overlooking the age gap between Ferb and Vanessa (but have an easy time overlooking the fact that Ferb and Gretchen have hardly interacted at all in the show itself). Yet the very second Monty is introduced as a love interest for Vanessa, Ferbnessa becomes more popular.
There is also a sizable set of Doofenshmirtz/Linda shippers, to the point that it's a YMMV/WMG that he is Phineas' father. Doesn't help that it's canon that they used to date.
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.
While many Randy Cunningham: 9th Grade Ninja fans ship what seems to be the intended endgame of Randy/Theresa ("Fowlham"), even more ship Randy and Howard ("Weinerham"), probably due to the show having all of the usual questionable bro closeness without so much of the "no homo" that usually comes with it.
T.J./Spinelli is incredibly popular, ever since their Practice Kiss in "The Experiment" and the confirmation on Spinelli's side in "Parents' Night".
Also Gus/Cornchip Girl, the Moe Couplet of the series. The Japanese title for their episode, "The Army-Navy Game", is "Gus's Girlfriend".
Vince/Gretchen also has a pretty big following, thanks to all the Ship Tease.
In Regular Show, altough Thomas and CJ never met, fans like pairing them together, especially from the Mordecai/Margaret fans. Some are the reasons are Thomas deserves a nice girl and it beats having the Mor/Mar fans bashing poor CJ. But since it was revealed Thomas' a Russian spy and went on the run, it's not known the current status if this ship.
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.
While the original '70s cartoon was No Hugging, No Kissing, most of the people at large assumed that Fred/Daphne were at least implied. Meanwhile remnants of Shaggy and Velma being siblings during the show's creation could have been interpreted as pairing of the two.
In the 80s the subtle hints shifted over to Shaggy/Daphne with the two even sharing a long hug in one episode.
Since then starting with Zombie Island, Fred/Daphne started being played with more directly to a split base.
In Sidekick, Eric has a crush on Vana, but fans like him better with Mandy or Kitty instead, never mind the fact that Vana would take any opportunity to leave Eric for dead, and usually needs serious coercion to help save him.
Star vs. the Forces of Evil: Even with its Broken Base status, it's undeniable that Starco was insanely popular from the get go. This includes Adam McArthur, Marco's voice actor, who is very openly shipping it. Fans were shipping it several months before the show even premiered.
Star Wars: The Clone Wars: 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.
Reef/Fin from Stoked is easily more popular than any other pairing on the show, even though Reef/Lo is the Official Couple as of season two.
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.
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.
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).
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.
Teen Titans: Beast Boy/Raven. The creators of the show repeatedly stated that Beast Boy/Raven would never happen, yet it was an increasingly popular to the point where it's considered intentional by a large chunk of fans and it's the 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), and popular enough to occasionally get a bone thrown at them in the mainstream comics. The animated comedy Teen Titans Go! has completly embraced the pairing, dedicating several moments and whole episodes to their relationship.
In Tiny Toon Adventures, Ensemble Dark Horse Fifi la Fume is occasionally depicted as the target of a crush by Hampton J. Pig. In the fandom, very few acknowledge this, as most prefer to portray Fifi finding love with her male feline classmate, Furrball. This stems predominantly from the fact that Fifi having a crush on Furrball is canon to one episode (although it goes nowhere, Furrball's dislike of Fifi as a Smelly Skunk has to do with her stench and he doesn't dislike her as a person), the fact that this would further Fifi's resemblance to her inspirationnote Fifi is a Gender Flipped expy of Pepe Le Pew, whose running (if somewhat reluctant) love interest is the female Penelope Cat, and the fact that Furrball is a sympathetically unlucky, unloved and abusedUnpopular Popular Character and Fifi is an Ensemble Dark Horse with a lot of love to give.
Sam and recurring villain Tim Scam also seems to be a popular ship among the fans, given that it takes up a good chunk of the Totally Spies archive on FF.net.
Transformers: Generation 1: Prowl and Jazz might well embody this. In canon, regardless of cartoon or comic, they barely interact, and the few times they do, they generally dislike each other, and yet they have hundreds of fics on FFN. There are reboots where the two are on good terms, but most of the fanfics pairing them are about the G1 characters. There doesn't seem to be any base to the pairing other than "they're both white cars from the 1984 line" and "they could have chemistry, theoretically." It gets to the point where Prowl/Jazz fans can get downright rude towards characters who do show affection toward Prowl (most famously Chromedome and the Constructicons).
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.
In X-Men: Evolution, while Scott/Rogue was a favorite of many of the shows creators (and had a large fanbase to speak of), fan support for Gambit/Rogue was so popular that eventually the writers gave an entire episode devoting time to the possibility, and the last image of the series suggested they were together. Interesting fact is that the writers, in the first scene Rogue and Gambit shared, had apparently intended to insinuate a past relationship between them (or so it is claimed); fandom was strong enough that if this plan was ever in the cards, it was discarded in favour of actually developing their chemistry onscreen, even if just for one episode.