The DC/Marvel series in the 90s gave us a short Robin (Batman)/Jubilee (X-Men) romance which was quite nicely done, in a rare example of a canonical crossover ship. note Made Hilarious in Hindsight due to the fact that the two were combined in the Amalgam Universe to become Sparrow.
One of the one-issue "giant crossovers" from the 1980s teased the readers with hints of Beast Boy (then "Changeling")/Kitty Pryde. Another played with the concept, possibly to parody it, by having Spider-Man ask Wonder Woman if she thought it was too early in their relationship to consider marriage (they had met, and briefly fought, only a few minutes earlier).
A Wolverine/Witchblade crossover licensed by Marvel and Top Cow started with Logan and Sarah Pezzini getting married! Obviously it didn't last.
It sees Kismet and Eternity, the avatars of the DC and Marvel Universes respectively.
It has Hawkeye and Black Canary, but only briefly and for the sake of a gag. A shift in the multiverse quickly puts her back together with Green Arrow.
The SyFy channel has embraced this trope, pairing up Claudia and Fargo in their Warehouse13 / Eureka crossover episodes. At first, it just seems like a mutual crush that won't go anywhere, but then, Claudia's boyfriend breaks up with her. Then, Claudia comes to Eureka. As they search for what's causing that week's problems, there is some flirting, and after being saved from a minefield, we get a full-blown makeout.
Setsuko Ohara of Super Robot Wars Z and Shinn Asuka of Mobile Suit Gundam SEED Destiny in Z is probably the most supported pairing, if not, the prime Crossover Ship in existence, as it's one of the few that makes a lot of sense considering their close relationship in-game. Because of the presence of Setsuko in the game and how Gundam SEED Destiny's events are rolled out in her route, Shinn's glaring flaws from the original story are actually fixed, or at least mellow them down. It helps that Setsuko can relate with Shinn on an emotional level. Arguably, this fanon pairing has become the best example of this trope. It helps that they actually do become very close in the game.
In a spin-off series in the Eighties and Nineties, it was implied that Nancy Drew and Frank Hardy had a crush on each other (Poor Ned and Callie). Similarly, there was a much more faint flirtation between Bess Marvin and Joe Hardy.
A throwaway panel showed Jafar (Aladdin) and Maleficent (Sleeping Beauty) at the same table — with Mickey whispering that the two were on a date. Disney fanatics instantly took a shine to the two as a couple.
If that doesn't work out, House of Villains and The Kingdom Keepers suggest that Maleficent and Chernabog of Fantasia would be great (and dark) together.
House of Mouse also gave us Hades having a bit of a crush on Maleficent. There's also potential in Black Pete, given his servant-like relationship to her in Kingdom Hearts.
Especially pairing Usagi with some other guy besides Mamoru. There are even two dedicated categories for Gundam Wing and Dragon Ball Z crossovers, mostly because the shows all aired on the Toonami block around the same time.
Usagi tends to get paired up with a lot of characters from other series, as this YouTube video proves.
Sailor Moon girls have an annoyingly frequent habit of getting paired with the Saint Seiya boys. There are reasons, of course-they're roughly equal in number, and there are so few females in Saint Seiya that if you wanted a het ship you'd probably have to use a crossover. Also, if you try you can get characters with matching hair colours to pair up together...
There are a surprising number of Sailor Moon/X-Men crossovers that run the gamut of serious to silly but one of the most consistent aspects is the shipping Sailor Mercury/Nightcrawler.
Theres also a lot of shipping for Nanoha X Madoka - A popular series to begin with since both series are highly non-conventional Magical Girl series who turned the genre on its head. Fate x Homura or Kyoko exists but is significantly less popular than Mado Nano.
It might be because of the pink energy from both of them.
Saber (Fate/stay night) and Kon (Bleach): She loves stuffed lions, he loves cuddling with anything female, and they would be adorable together.
Ozymandias plus Oscar Wilde. Wouldn't they be perfect for each other?
Ozymandias/Alexander the Great/Hephaestion threesome. Enjoy.
From Incredible Hulk and X-Men: Evolution: Hulk's Big Damn Heroes moment in Episode 3, Hulk/X-23. This one technically isn't a crossover ship as the two exist in the same continuity. Though it is pure crack, as aside from the age difference (she's 16, Hulk's pushing 40), the one time these two have met involved Hulk beating the hell out of her friends and throwing her through a building.
Ariel and Peter Pan. If you think about it, Disney hasn't had that many redheaded couples.
Peter is also paired up with Melody.
The more famous pairing with Ariel is with Jim Hawkins.
Film — Animated
There are plenty of people who ship Jack Skellington from The Nightmare Before Christmas with Emily, the Corpse Bride from the title. For people who like their fan fic slashed, there is Jack Skellington/Victor Van Dort, Emily's very much alive "husband" for a time. Emily the Corpse Bride gets paired with Sally the Rag Doll from Nightmare, who is a cute rag doll created by a Mad Scientist. For the Jack/Emily shippers who don't want to leave Sally alone, they've paired her with Bonejangles, a skeleton musician from Corpse Bride. The two films just go well together.
There's a rather disturbing pairing: Jack Skellington of The Nightmare before Christmas and Coraline of Coraline. That's right, an eleven-year-old girl with a fully adult skeleton.
An age-appropriate crossover pairing with Coraline is with Norman of 2012's ParaNorman. It may have something to do with Coraline having brown eyes and blue hair and Norman having blue eyes and brown hair.
Olivia Flaversham from The Great Mouse Detective and Fievel Mousekewitz from An American Tail is one of the few age-appropriate shippings Olivia ever gets without being aged up. Fan art and fan fiction tends to play up the pairing's sheer adorableness.
Merida and Rapunzel have been paired with each other.
And for completion's sake, Rapunzel/Hiccup has also been made.
Despite Elsa not being part of "The Four", she's starting to get shipped more often with Jack, not just because they're both ice people, but also because Jack's playfulness contrasts very nicely with Elsa's seriousness.
This fan fic "Lioness Abroad" has Vitani (The Lion King) and Alex (Madagascar), when Vitani gets captured and sent to the Central Park Zoo. It makes a lot more sense then most of the stuff on this page.
It's only a little exaggeration to say that characters from Harry Potter get shipped with every other available fandom out there. Especially Harry Potter gets paired with female characters, but there is also lots of Slash.
There's an awful lot of Harry/Buffy fiction out there.
It's definitely a thing in Jane Austen's fandom to pair up people who remained single, and very often cross-novels. It helps that the world of Jane Austen's books is always very similar — pastoral and almost-idyllic version of Regency England. It's not uncommon for characters like good-natured but stupid and extremely wealthy Mr Rushworth of Mansfield Park, divorced from his cheating wife, to be paired with Miss Bingley from Pride and Prejudice who was always after money, or some ship him with Mary Bennet, who, as some fans believe, deserves more attention and a wealthy husband.
There is one extremely weird example of, of all things, River Tam being shipped with Heat. It stemmed from the two encountering one another during a multi-author Mega Crossover, with Heat equating River with Sera. She latched on to him because he was protective of her, he latched onto her because she reminded him of Sera. Things got even weirder from there, with Heat doing his cannibalism thing and River being not-at-all freaked out about it. The thing had a rather powerful and sad Did Not Get the GirlDowner Ending, as there wasn't any sex, just very rough kissing (with biting and some bloodplay involved) and a whole lot of insanity, and the two had to split apart at the end of it because Heat refused to take River back to a world as screwed up as his and had no place in hers. It was really well-done, especially on the part of the author writing Heat's part of the story.
There are a few Buffy/Firefly crossover fics that ship Spike with River Tam. This works remarkably well as crossovers go. Spike, who spent over a hundred years with Drusilla and was then haunted by the First Evil, has significant experience with people who "see things" and is in a better position to relate to River than anybody in Firefly canon. Spike's immortality makes it easy to rationalize his presence in the Firefly universe: he just lives long enough to leave Earth-That-Was with the rest of humanity. Then there's the fact that having been born in Earth-That-Was makes him an (un)living memory of a time that is seen as legendary by the inhabitants of the 'Verse.
There's a growing number of River Tam (Firefly) and Riddick fics.
Thanks in no small part to a little fanfic called The Way of Things, Rose (Doctor Who)/ DI Carlisle (Blackpool) has an impressive following.
There was once a movement on LiveJournal to pair Captain Jack Harkness of Torchwood and Doctor Who with every single fictional character ever. Unsurprisingly, it didn't complete its task, and later it lost steam altogether.
Buffy the Vampire Slayer has sometimes been shipped with Dean Winchester of Supernatural, or sometimes with Sam. So has Faith, for that matter, though both Slayers more likely end up with the older brother. In a case of Pair the Spares, if Buffy is with Dean then Dawn will likely be shipped with Sam. The pairing is strengthened by the idea that the two universe actually mess together rather well, with the metaphysic differences not too hard to Handwave due to having a number of common elements.
Dean (Supernatural) gets around. The most popular het ships are Dean and Chloe from Smallville and Dean/Hermione (Harry Potter).
It can be quite safely stated that there is an entire sub-category of Smallville fanfiction devoted to the idea of Chloe moving to Gotham City (often after the author has Chloe realize that Clark/Jimmy/whoever "isn't good enough for her") and then meeting and falling in love with Batman. Usually, Chloe ends up either becoming Mission Control at the Batcave or she undergoes Xenafication and becomes Batgirl or Batwoman (or occassionally Catwoman) and ends up fighting crime alongside Bruce on the Gotham City rooftops. Either way, she can usually work the Batcomputer better than Bruce can, proves to be his match in fighting skills, and if Bruce is still "in denial" about his feelings for her, Alfred will usually advise him to "open his eyes and see what's right in front of him."
With the addition of Victorious, Cat/Freddie and Jade/Sam are quite popular. The idea that a Drake & Josh/iCarly crossover might happen also fuels Freddie/Megan support.
With the new crossover Spin-Off show Sam & Cat featuring Sam from iCarly and Cat from Victorious, it took all of one episodes for people to start shipping them together.
Chloe (Smallville) is a Launcher of a Thousand Ships (possibly due to the huge amount of fanfic writers who seem to very strongly relate to her personality), and another hugely popular Smallville crossover ship is to pair up Chloe with either Dean or Sam from Supernatural (or, y'know, both). The Chloe/Dean ship seems to be more popular than Chloe/Sam for whatever reason.
This video ships Lieutenant William Bush (Hornblower) and Miss Molly Gibson (Wives and Daughters). Regency England, a handsome naval officer and a pretty little young lady. It's very adorable and believable. There's a severe lack of ladies in Hornblower, the series being all Wooden Ships and Iron Men, so it's logical that these wonderful sailors would look for love in other book or TV 'verses.
Martin Crieff (Cabin Pressure) / Molly Hooper (Sherlock) has a modest following. Cabin Pressure and Sherlock are Friendly Fandoms that are easily crossed over. Depending on the execution, it can be a combination of Theme Pairing and Throw the Dog a Bone, as both Martin and Molly are rather unfortunate in many aspects of their lives and overdue for something nice to happen to them. (There's also the fact that Molly pines after Sherlock, who's played by Benedict Cumberbatch, the same guy who played Martin Crieff.) There also seems to be a small but steadily increasing number of fans of Martin and one episode character Henry Knight.
This fic crosses over Stargate SG-1 and Torchwood. Pairings include Jack Harkness/Daniel, Jack O'Neill/Ianto, Owen/Anise/Freya, and Gwen/MALP. Bonus points for the title being abbreviated to CR:ACK.
Irene Adler (Sherlock) / River Song (Doctor Who). Two badass ladies of questionable morals together at last. And both shows have Steven Moffat as the head writer.
Sort of happened in S.O.L., in which, due to accidentally drinking a pheromone potion, Scully spends a lot of the story hitting on/making out with Joel (Much to Joel's dismay). Even after she's cured and apologizes to Joel, she kisses him at the end of the story, and Mulder teases her about it.
A staple of "multifandom" Journal Roleplay games. Since these games dump characters together into one common setting, they can become Serious Business (particularly since LJRP itself is serious business), although they're often suggested for simple crack as well.
Lynching ITP occasionally brings some wacky crossover ships including:
Anders / Kain has been sighted (the fic in question had them meeting in the Fade somehow). Maybe it makes some kind of cracky sense given their common status as party members straddling the hero/villain line, but that's about it.
Pairing Noctis of Final Fantasy XV and Lightning of Final Fantasy XIII (which, despite names, are set it totally different universes) is surprisingly popular, and has been even before the release of either game, if FF.net is any indicator.
Makes sense considering the working title for FFXV was "Final Fantasy Versus XIII." It was only later revealed to be in a separate continuity as the next full sequel.
Morrigan seems to be switch-hitting between Tony and Chris in the openings. In the Episode 2 trailer, after Iron Man saves Viewtiful Joe but fails to do the same for Amaterasu, Morrigan saves Ammy and then blows a kiss to Iron Man. In the Episode 4 trailer, the last shot is a still showing all of heroes and villains duking it out... except for Morrigan, who is seen lovingly wrapping her arms around a flustered Chris, perhaps as a way ofsaying thanks for saving her in Episode 1.
There's been a boom in Dante (Devil May Cry)/Morrigan (which had been around at least a few years prior to MvC3); it's probably Dante's most popular ship next to/alongside Dante/Bayonetta.
In a Mythology Gag to Dante's meeting with Nevan (yet another Horny Devil) in Devil May Cry 3, the two are seen flirting if they're on point against one another. Dante's also says, "Mmm, baby. I love it when a girl gets violent!" at his win screen should he defeat Morrigan last in battle.
In C. Viper's reveal trailer (Street Fighter IV), Iron Man is hitting on C. Viper in the pre-match intro, causing some to ship them as well. Iron Man and Morrigan seem to launch ships left and right.
Iron Man hits on every female in this game not named Amaterasu. This includes Tron Bonne and X-23, who are respectively 14 and 16, as well as Hsien-Ko, who is (technicallyspeaking) dead. Fans jokingly suggest that the only reason he doesn't go after Ammy is because he doesn't know that Ammy is a she. Should he win against any of them, he muses, "Told you... a nice candlelight dinner would've been better." Should he win against Morrigan, his quote at the win screen reads as such:
"I think we can sort out our differences over dinner. I'll have the best chefs flown in."
Felicia (Darkstalkers) and Super Skrull (Fantastic Four) appeared together on one game-affiliated t-shirt. Cue the fans on Capcom's official forums shipping them together.
Thanks to the Episode 4 trailer of MvC3, Final Fight's Haggar/Felicia.
Felicia has a humorous win quote against Deadpool: "No, I don't care how much catnip you have, I'm not getting into the car with you!" How you interpret this one is up to you.
Morrigan apparently has a fancy for Wolverine (her quote at the win screen reads, "You have a beastly charm I just find so, so intriguing"). She also cameos in his ending as an exotic dancer trying to seduce him. Wolverine relents to her whimsy... but not before he finishes his drink.
Crossover Shipping in this seriesactually happened beforeMvC3. As early as Marvel vs. Capcom 1 did Gambit's ending have him flirting with none other than Morrigan (her total number of ships, excluding a few dubious examples in 3note she has some Les Yay-ish intros with X-23, Tron, and Phoenix, as well as some ambiguous quotes towards Magneto, is up to eight right now, if you lost count). Before anything can get off of the ground, Rogue swoops in to carry Gambit away, much to Morrigan's displeasure.
Shuma-Gorath displays a creepy fondness for Hsien-Ko, going as far as to propose to make her his bride. Also, Morrigan herself shows an interest in Shuma's tentacles.
In Ultimate, Morrigan blatantly hits onPhoenix Wright. Blatantly. And then there's Rocket Raccoon having the hots for Ammy... By the way, 95% of the examples above come from the game itself. This isn't even getting into Fan-Art. Marvel vs. Capcom 3: If it breathes, this game will ship it.
There's a fairly big fanclub for Danny/Juniper Lee (The Life and Times of Juniper Lee), though some find it squicky because of the age difference. Though once June is aged up from 11 to 13, there is less Squick.
Danny and almost every Disney princess has more than likely been done at least once in the Cartoon X-Overs section on Fanfiction.net. That is, whenever they're not being paired with Sora from Kingdom Hearts or Ash Ketchum from Pokémon.
Tumblr once exploded with Norman (ParaNorman) and Dipper (Gravity Falls) fanart tagged under Parapines. This mostly seems to stem from their supernatural connections and general adorableness. So far, the art remains rather tame and limited to G-rated interactions like kissing. Examples: . The Norman and Dipper shipping grew into a sort Multi-player crossover entitled Mystery Kids or Spook Crew. Members include but are not limited to Dib, Raz, Coraline, and Courage Examples: 
Steven/Mabel is starting to grow in popularity, as well.
Lisa Simpson from The Simpsons is the Launcher of a Thousand Ships in some crossover fics. She's been paired up with, to name a few, Dalek Sec, Starscream, Waspinator, Jack Harkness and Randall Boggs of all characters, although, with the exception of Captain Jack, those were all subtext.
While not as common as most others, Lilo from Lilo & Stitch has ocassionally been shipped with Mac from Foster's Home for Imaginary Friends due to a couple of similarities they have (being bullied, having a crazy non-human blue friend, etc.).
Lots of pairings combining the pony show with Team Fortress 2: Applejack with Engineer, Rarity with Heavy and Spy, Pinkie Pie with Soldier, Pyro, Heavy and Scout, Fluttershy with Medic and Heavy, Rainbow Dash with Scout, and Twilight Sparkle with Sniper via Youtube.
Semi-related, unpopular example: Pinkamena Diane Pie from the infamous Cupcakes and Audrey II from Little Shop of Horrors have been paired together. Yes, there's a pairing between a murderous, fun-loving pony who enjoys torturing her subjects and a manipulative, singing, man-eating plant that needs blood to live. This unholy union may doom everypony, but they'd make a killer duet.
A common meme: Derpy Hooves/Doctor Hooves. Semi-arguable; there is a pony in the show who (somewhat) resembles David Tennant (and launched SO many memes), so whether this is a full crossover or not is the debate point; some fics treat him as the Doctor if he had always lived in their 'verse, others have him arriving and dealing with life in Equestria.
Azula left Doom, complete with a "Dear John" letter. Apparently the good Doctor has rebounded and is going out with Squirrel Girl, but rumors of Azula returning are flying around.
Prinack- a couple consisting of Jack Spicer (Xiaolin Showdown) and Teen!Princess Morbucks (The Powerpuff Girls) was made popular by Deviantart artist,Callyie-Chan She draws most of the fanart and has a medium following by the Powerpuff Girls fandom, and somewhat of the Xiaolin Showdown fandom as well. There is a fan club also.
This couple could also count as a Theme Pairing due to the following tropes.
Harmless Villain: There was a episode where Blossom regarded Princess as such and we all know about Jack.
Parental Neglect: Jack's parents are never there and we never see Princess' mom. It might be implied that her parents got divorced or she works overseas a lot. Also, King Morbucks doesn't seem to have an interest in her well-being and he's only around to give her money when she asks for it.
Lonely Rich Kid: To an extend. They both don't have siblings and nobody really likes them much. It's also impiled that Jack comes from a wealthy family like Princess. That would explain his fancy house and he ability to build almost an unlimited amount of robots.
Da Ji regularly hits on Sakon in the second game's Dream Mode levels. Guo Jia/Ina gets some shipping going on in the third game despite the fact that Ina is both canonically and historically married to Yukimura's brother.
Cloud / Terra has a following as well, as do Firion/Terra and Firion/Cloud. Why these three? Besides Cloud's interactions with both of them, Dissidia heavily implies that Firion and Terra remind Cloud of Zack and Aerith, and their personalities are reminiscent of them as well. It didn't take long for shippers to go from there. It helps Terra has no canon love interest.
The prequel, Duodecim, gives us Firion/Lightning due to their mutual bonding over flowers. Comes complete with Ship Tease, as Cecil (the only canonically married member of Team Cosmos) plays the role of Firion's wingman and takes his embarassment over wanting to talk to Lightning as romantic interest.
Correction: JediAnnSolo has repeatedly stated that Sandy/Shadow is not Agency canon. However, this hasn't stopped her from admitting that they make a good couple or stopped her and her fans from pairing the two up.
Tails/Klonoa seems to be a relatively popular one amongst the Furry Fandom, perhaps inspired by a certain doujinshi featuring the two... ehm, hanging out after work. That the two already looked similar doesn't hurt, either.
Damon Salvatore/Blair Waldorf shouldn't work, but the reasonably large number of Youtube videos beg to differ
Sometimes you go for obvious subjects, but sometimes some authors want to make up perverted situations that normally don't exist. How about a hentai fanfic featuring Cecilia and Noblesse Oblige or Harken Browning making Cecilia wear Kaguya's stripperific outfit just to bang her in it?
In this Spider-Man/Danny Phantom crossover  the author pairs Valerie Grey and Johnny Storm. kinda squick-ish because Valerie's in high school and Johnny is supposed to be Peter's age (if not a year older) which leaves quite a large age gap.