There's a whole community dedicated to the love of Zhao (as in Admiral Zhao) and Hahn (as in Princess Yue's fiance who appears in the S1 finale). Their only interaction was Hahn trying to ambush Zhao after disguising himself as one of Zhao's soldiers, but ruining it by loudly announcing his attempts to kill "Admiral Choy", then being casually thrown off the ship. In their own words:
Some (Not saying any names)LiveJournal communities make a goal of finding the biggest crackships in the fandom. So far there's Yue/Chong, Appa/Momo, Appa/Bosco, and so forth. They occasionally even shipped them with members of the production crew... which one of them stumbled onto. Then there's Ba Sing Se/The Drill, Aang's old glider/Aang's new glider, Roku/Volcano, Mako/Mako's scarf, The Cabbage Merchant/cabbages, the owlcat from "Tales of Ba sing Se"/the owlcat from "The Puppetmaster", Joo Dee/Ozai, Jet/Zhao (although that one kind of makes sense, seeing as how they're both dead)... the list goes on and on and on.
While probably not the most crackiest pairing in the fandom, Azutara (Azula/Katara) deserves mentioning as it is not as uncommon as you would think. This shows quite well (albeit in a rather funny manner) what fans like about it, y'know, besides the 'Two lovely ladies getting it on' factor.
Zuko/Lt. Jee has a surprisingly devoted fanbase.note For those who don't remember who Lt. Jee is, he's this guy,◊ the one who yelled at Zuko for wanting to sail into the storm. Despite the fact that Jee had about four minutes of screen time, there has been a ship week, one WIP long fic of incredible quality, and a few other small fics and illustrations scattered across the fandom. This pairing seems to be unusual in that the fanworks for it are all very well-done.
Azula/Sokka from How I Became Yours. Of course, this is helped by, the fic having Azula lose her memories and get her entire personality to be rewritten, and after almost dying, Azula comes back with white hair that makes her look just likeYue.
The show had crack pairings develop well in advance of airing, in particular, Korra/Yue the Moon Spirit with a separation of 70 years and a metaphysical plane proving no obstacle to the pairing's Memetic Mutation on deviantArt. The progression seems to have been "Avatar rides spirit guide->Spirit guide is usually the thing that taught their culture bending, like dragons for firebenders and bison for airbenders->Moon taught waterbenders->Yue is the moon now->Korra rides on Yue->Korra and Yue ride each other."
Danny Phantom has tons of them. The best one has to be Danny/Fenton Thermos. It was started to poke fun at how ridiculous the ship wars were getting, but it caught on. There are also MANY Danny/OC pairings.
Transformers fandom in general is made up of crack pairings, often with characters who have had little or no interaction in the show/comics. There are very few individuals who haven't been paired with someone at some point and often in very bizarre combinations. This is probably at least partly the fault of the Transformers Anonymous Kink Meme.
South Park: In-Universe, there's Tweak and Craig. Note that a) they're both male and b) neither one of them is gay. They were upset enough by it to stage a breakup to get their classmates to stop pairing them, but that didn't go so well either (turns out Tweak had a hidden talent for acting, so for Craig it went from "being annoyed that everyone thought he was gay" to "being annoyed that everyone thought he was gay and a jerk").
SpongeBob/Krabby Patty, although it was intended as parody, still seems wrong. Even better in the canon episode in which this happened. SpongeBob ends up murdering a flock of clams to protect "Patty" from being eaten.
Even earlier, in the episode "Just One Bite", Squidward has a dream/fantasy sequence where he falls in love with and marries a Krabby Patty.
There exists a fan-film named William Country, that has Cody/a Palette Swapof him. The only difference is that the swap has black hair (bad by its own, Cody has brown.), and his hair is messier (well, the hair and the clothes, but still...). Screw Yourself, anyone? The best part is that the Fan Film is said to be 90 minutes long, and the remaining clips not taken down (see on the page) add up to quite a bit. And it has good animation, almost matching the show's style. Yes, someone put that much work into a fan fic of Cody being gay with himself. Think about it.
Total Drama World Tour gives us a potential (one-sided) Canon crack pairing: Noah / Bridgette.
One writer ships Heather and Staci—two characters who have nothing in common and have never met in canon—precisely because it was the most absurd Total Drama pairing she could think of. For all that, the writer somehow managed to make it work.
The Kim Possible fandom has a few favorite ships that can be considered crack.
Kim/Rufus had one story written for it, a story so infamous that it was banned in less than a day and still causes some of the older members of the Kimmunity to wince when they hear the line "Oh YES! Rufus, you ARE the Tunnellord!".
Vacation From The Norm features several crack pairings, but in most cases makes them work in their own weird way. By the end of volume 1, we have; Kim/Ron/Shego, Drakken/Vivian Porter, Motor Ed/Yori, Joss Possible/Felix Renton and Gemini/Betty Director It's implied early on that Betty Director was replaced by an imposter. It's later confirmed that the imposter is the Humanshifting villain Camille Leone. The real Betty Director hooks up with Will Du.
For a canon example, the episode "Stop Team Go" featured Shego/Mr. Barkin. Granted, the former was under the influence of a Mirror Morality Machine at the time, and she breaks things off (violently) when she returns to normal at the end of the episode.
The Adventure Time fandom has Gumgrab- Prince Gumball and Lemongrab. Prince Gumball is basically a pink Prince Charming, and Lemongrab is a strident, socially retarded jerk who has a completely repellant, obnoxious personality. It all started with a crack comic on deviantART and three fateful words: "THREE HOURS BEDROOM!" Even Rebecca Sugar, a writer on the show, "liked" the original Gumgrab comic on her Tumblr, and commented: "Well aren't you forward, Lemongrab!" What makes this pairing weirder are the ambiguously incestuous overtones. Prince Gumball is a genderswapped version of Princess Bubblegum- who created Lemongrab in her laboratory- and the prince is also, in-universe, a fictional character created by the Ice King for his fanfiction. People are shipping Lemongrab with his father from a parallel universe that doesn't even exist.
The episode "All the Little People'' has Finn create several of these with tiny duplicates of the series' characters. At the beginning of the episode he and Jake also jokingly discuss Ice King/BMO, and by the end of the episode the tiny duplicates of those very characters hook up on their own.
Included in a possibly Squick post on Usenet newsgroup is a story which includes a crack pairing of Liono and Snarf of ThunderCats which is certainly NSFW even though text-only.
One of the more notable examples early on was Octavia Melody being shipped with Vinyl Scratch. They had only appeared in the show for a few seconds each, and weren't even in the same episode (or town, for that matter). Despite this, a large number of fans declared them as their One True Pairing, simply because they both have musically-themed cutie marks and different musical tastes (Octavia is a classical musician and Vinyl is a techno DJ); creating an Odd Couple dynamic that was played with in a number of fanfics and videos, most famously Epic Wub Time. As of Episode 100 "Slice of Life", Vinyl and Octavia were shown living together in the same house, making the ship effectively canon.
On the Derpibooru image board there is a tag called "Twilamp" for art and short fiction depicting the passionate relationship that Twilight Sparkle shares with the lantern that hangs outside one of the windows of the Golden Oaks Library where she lives.
Invoked by the writer of the MLP fanfic The Conversion Bureau: The Other Side of the Spectrum, in which he pairs Lightning Dust and Rainbow Dash (It's mentioned in chapter 6) together. Apparently, they now work together as leader and wingpony, ( Probably helped along by Bag of Tirek-induced brainwashing, and the fact that Spitfire resigned from the Wonderbolts in disgust.) with rumors that their relationship is a bit more than professional. Therearesomanyreasonsthatdoesn'twork. Then again, considering the TCB!Ponies, it's not like she'd stand out...
The Great and Powerful Trixie and Maud manages to be among the most popular ships involving Maud Pie despite the two having very few connections/similiarities, except for being friends with Starlight Glimmer.
Pinkie-Pool. Pinkie Pie X Deadpool. Still a crack pairing, but perhaps not quite as insane as it initially appears to be given that both characters are notorious for breaking the fourth wall.
The animation Strangers ships Sweetie Belle and Button Mash together. The two don't have anything in common besides being foals from the same town. Button Mash is little but a background extra. This ship is popular due to Button's Adventures depicting the two drinking milkshakes together.
Claro de Luna pairs together Princess Luna and Octavia as a Theme Pairing. At the time of the fic's publishing, Octavia was only a background character in one episode (and an episode that Luna wasn't even in, at that).
In The Royal Sketchbook, Celestia eventually falls for Rarity and the two begin dating. In canon, they have a near-strictly professional relationship and rarely interact one-on-one.
Unfamiliar Patterns is a fanfic that pairs together Rarity and Zecora. It's considered crackish even in-universe.
Marge Simpson Anime not only has Marge falling for Maude, but she leaves Homer for Abu's wife Manjula.
This comic by Panic Volkushka depicts Bart Simpson and Chris Griffin going to couple's therapy. And it's actually really damn good, realistically discussing the baggage they must have from growing up with abusive fathers.
The Foxbusters: The episode "Winging It" shows some romantic subtext between Todd (a fox) and Jefferies (A chicken). Yes, bizarre and cracky but also completely adorable when you think about it as Todd is a lovable ditz while Jeffries is a comic relief and both are highly Adorkable.
In-universe, we have the Official Couple of Kid Flash/Jinx. Worked just fine in the cartoon. Odds of it ever happening in the comics are nill to non-existant.
The New Batman Adventures episode "Love is a Croc" gave us a very disturbing pair-up between Killer Croc (an eight-foot-tall Beast Man) and Baby Doll (who Can't Grow Up and dresses like a five-year-old). Granted, Croc was just using her, but Baby Doll's affection was entirely genuine.
This is even played with in the show, when the Mistress hooks up with Lord Stingray on a whim after taking over the jail. Jared and Charise then attempt to get her to sleep with the Warden to fulfill their own chance of being together, but their hopes are shot down when Alice does so instead. Though some Warden/Mistress fans cried foul after the episode, it spawned fans who began to pair Mistress off with the new option (even though in all likelihood, it'd be one-sided on her part).
Frostbackscat has a thing for Ms. Frizzle x humanized Bus, and even has pictures of it on her Tumblr page.
While it was only for a school play, there still was an episode of Codename: Kids Next Door where the play's main couple was played by Numbuh 3 and the Delightful Children from Down the Lane. As in, all five of them.
Ed, Edd n Eddy: In-Universe, the conflict in the special "Hanky Panky Hullabaloo" came about because a pair of cupids (that looks suspiciously like Jimmy and Sarah) forced Double D and May together. The climax involves the cupids, in an attempt to stop the fighting between the Eds and the Kankers, force other crack pairings: Kevin/Lee, Nazz/Johnny, Ed/Sandwich, Eddy/Plank, and a one sided Marie/Rolf. Rolf, who avoided all the cupid arrows, snaps everyone out of it by throwing dirty mop water on them.
Blueswap AU is an entire fanverse about pairing together Greg and Blue Diamond. In canon, Blue Diamond sees human as little more than pets and doesn't interact with Greg. In the AU, Blue Diamond switches roles with Rose Quartz, falls in love with Greg, and has Steven with Greg.
Done In-Universe in The Amazing World of Gumball episode "The Shippening". In this episode, Sarah buys a cursed notebook from the Awesome Store that makes whatever she draws therein come to life, unbeknownst to Sarah herself. This being Sarah, she draws numerous Crack Pairing scenarios in the book, unknowingly igniting a wave of bizarre love stories all over Elmore.
Miraculous Ladybug: The two of them barely interact in canon, and their few interactions so far have been entirely negative, but for whatever reason Chloé x Kagami has become a popular ship in the fandom. This one has shades of Pair the Spares; both of them are alternate love interests for Adrien, so pairing them up would remove some obstacles in the path of him hooking up with Marinette. Curiously, it's also common in anti-Lila fics, where the two are often made into Marinette's allies against Lila's plots.