"The most exciting attractions are between opposites that never meet." — Andy Warhol
So you like to ship Bob and Alice. The only problem you have is the fact that Bob and Alice have exchanged little more than a few lines with one another, there seems to be little to no interaction between the two, or they may be no evidence that they've ever met each other.
This is when Ships Pass in the Night. Most of these types of ships are Crack Pairings, but as usual Tropes Are Tools — sometimes fans can dig deep and find decent proof for their beloved ship, or at least persuade the readers that the couple would give each other the time of day. Even without this a pairing can work if written well enough, but if no transition period is shown the couple is suddenly Strangled by the Red String.
Compare Launcher of a Thousand Ships, which can be a cause of many of these kinds of pairings.
Named in a remark made by Donald Hogan in Stand on Zanzibar.
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Anime and Manga
Most ships in the Pokémon anime fandom are nevermets, have something to do with filler characters, or with characters who have had little interaction with each other. Here is a long list of the anime's ships, including "never-mets". Most of them, the characters only interacted during one episode; James saves Cilan once, James/Cilan is born; Max talks to Misty, Max/Misty is born; and so on.
Dawn and Paul, despite how the two rarely speak and when they do, it's the farthest thing from romantic (he once even forgot she existed).
Misty/Gary was popular in the old days.
Of course, Ash has been shipped with plenty of girls that he met at only one time.
Tiger & Bunny: Ivan (OrigamiCyclone) and Pao Lin (DragonKid) hits the fandom HARD, probably an extreme case of Pair the Spares. However, the manga adaptations of the anime show that Ivan and Pao-Lin are indeed friends and do spend time with each other. Also, the official guide book "Hero Gossips" contains interviews with all the characters and there Ivan claims that Pao-Lin is the hero he's most friendly with.
Kakashi/Iruka is a very popular pairing, even though they haven't interacted that much, not even having met at all when the pairing became popular. Some people responsible for Naruto merchandise had seemingly latched onto this Fan-Preferred Couple and produced an astounding number of merchandise with only the two of them (these included, back in 2006, posters, mousepads and mugs).
Kakashi/Anko, who have occasionally been in the same room together, but have never spoken.
Some fairly well-known ships are between characters who never speak at all. Sasuke/Hinata (pictured above) is one such example, even though Hinata only talked about Sasuke once in the manga. Of course, a fair potion of that ship's popularity might stem from the fact that it removes the two competing love interests for the the Naruto/Sakura pairing.
Rima and Utau from Shugo Chara!. No, really. There is a whole fanbase of them together out there.
Eriol and Tomoyo from Cardcaptor Sakura are a textbook example. They have a handful of conversations, all about other people, and the numerous fans take that as a sign of deep connection and possibly also current affections. Not to mention the fact that in the manga, Eriol/Kaho is indicated as canon and Tomoyo was in love with Sakura. The less popular ships Touya/Tomoyo, Touya/Meiling, and Eriol/Meiling are even better examples, as the two halves only interact on one or two occasions.
Asuka/Kaworu seems to have some popularity, despite the two never interacting in canon. This is probably because of a combination of non-Shinji/Asuka writers Cleaning Up Romantic Loose Ends, and the comedy value of Asuka's Tsundere nature struggling against Kaworu's Dissonant Serenity.
Shinji is paired with everyone, but Shinji/Hikari is the best example — it's one of the most common Eva crack pairings, but her and Shinji barely know each other. Although with her being Asuka's best friend and Toji being one of Shinji's friends, they at least have some chance of social contact.
Shinji/Maya isn't anywhere near as popular, but it crops us disproportionately frequently.
Rei/Kaworu. They never talked, and Rei said exactly two lines relating to Kaworu. Again this is a Pair the Spares situation, this time in support of Shinji/Asuka.
Although most likely a deliberate-joke Crack Pairing, there's also Rei/Rei and Rei/Rei/Rei, despite the fact that Rei I is killed by Ritsuko's mother before the series, and that Rei III is introduced after Rei II dies. This ship/OT3 can expand near-infinitely with the Rei clones in the dummy plugs and the Reiquarium. And the fact that Rei I may well be the soul inside EVA-00.
There's at least one fic where, among other pairings, Ritsuko and Kensuke are paired up.
Despite that Ren and Pirika barely talk to each other in either the anime or manga and that the Distant Finale of the manga implies that Ren's wife is actually Iron Maiden Jeanne (which is also an example of this trope), they seem to be incredibly popular as a couple, with the half of the fandom that doesn't dislike Pirika supporting the pairing. The reason for this is most likely the comedic potential stemming from how that Pirika's brother Horohoro and Ren fight almost constantly.
Horohoro/Tamao is also a fairly popular pairing, even though (in the manga at least) they've barely talked to each other. Again, Tamao is considered The Scrappy to one part of the fandom, but not in the part that supports this pairing (or Tamao/Yoh, which has a lot more of a basis in-canon).
The Axis Powers Hetalia fandom can be justified in doing this, since the characters are countries and the story is based off of history. Even if the author has not covered a time where the nations interact, fans can call upon their history classes or The Other Wiki for evidence of their ship for fan works. A list of them can be found here
There are quite a few fanfics for Renji/Tatsuki. In the Manga or Anime have those two had ever had even one conversation with each other?
There's a small following for Renji/Orihime, mixing with Ship Mates if it comes from Ichigo/Rukia fans who don't want bash them to get them out of the way. While it is true that Renji followed Ichigo's quest to save Orihime alongside Rukia, they haven't really interacted either.
Toshiro/Karin, despite their only interaction being in a couple of anime-only filler episodes.
Kenpachi/Unohana, started as this, only given any consideration because they figure the two have had to interact with each other at some point because of how prone Zaraki is to getting huge, bloody wounds. Then came The Reveal that Unohana is the first person to hold the title "Kenpachi", and Unohana called Zaraki the only man to who have brought her true joy.
Ukitake/Nemu seems to be gaining a nice following. As does Byakuya/Yachiru, thanks to their interaction during the Shinigami's Cup omake, as well as a severe case of Older Than She Looks as Yachiru is apparently close to fifty years old.
Ikkaku/Nemu, based on a single panel in which they smile at each other while Ikkaku is getting medical treatment, as well as Nemu objecting to Mayuri interrogating him.
Most of the Arrancar pairing are like this, as they rarely interact with each other. Stark/Harribel (who appeared several times in the same rooms but never spoke to each other, though it has been confirmed that they did get along perfectly well) and Grimmjow/Nelliel (whose sole interaction is Grimmjow kicking and yelling at Nel) are the two most famous examples.
Silent Shipping. Kaiba and Shizuka are shipped because of one scene in which Kaiba agreed to get medical treatment for Bakura because Shizuka openly begged him to do so.
Ryuzaki and Shizuka, who have never met and probably don't know the other even exists. The pairing was likely spawned PURELY out of the fact that Jounouchi would flip a shit, causing angst or comedy, depending on the writer.
Higurashi has Keiichi/Satoshi shippers... even though not only do the two never meet (until Kira comes out), but Keiichi is more of a Lovable Sex Maniac and Satoshi was a more serious Expy of Keiichi to begin with.
Yomi and Sakaki from Azumanga Daioh are a semi-popular ship, even though the two barely exchange words with each other.
Kurama/Yukina - they only exchange lines once in the anime.
A far more popular example is Kurama/Botan. While they interact a bit more than the above pairing, it's never much (at least not in the manga). This may be an example of Ship Mates, since every other member of the main group has a romantic interest (Yusuke/Keiko, Kuwabara/Yukina, Hiei/Mukuro) except these two.
There's more than a few Rolo/Euphemia fanfics out there. Euphie was killed off before Rolo was even introduced as a character and almost certainly never met him or even knew of his existence.
Rolo/Nunnally at least get some cute interaction in official art, but it's unknown whether the two ever met, and Rolo wanting to kill Nunnally kind of puts a damper on the whole shipping thing.
Rolo and Nunnally interact in Nightmare of Nunnally, although in that case, Rolo is a clone of Lelouch conditioned to think that he is Lelouch and Nunnally's brother, and has a significantly different appearance, personality and role.
There's a small but growing group of Princess Tutu fans who think that Autor / Pique and Femio / Lilie are viable pairings. Partially due to Cleaning Up Romantic Loose Ends (with Autor and Pique's crushes on Rue and Fakir respectively), and partially just for the sheer crack that would develop (Femio's self-obsession and Lilie's sadism).
Pairing up Kagome and Sesshomaru is incredibly popular within the fandom. No one seems to care that he shows little to no interest in her and tried to kill her/did not care if she lived or not early on, and she does not show any feelings towards him either.
Pairing up Kagome and/or Sango with the Band of Seven's leader Bankotsu, even though he never had any dialogue with either of them; it's more about the chemistry between their personalities.
Sango/Inuyasha, which seems to come out of the clear blue. The two very rarely speak directly to each other, unless its regarding Kagome or Miroku, in the entire course of the series. Granted there is one episode where they get drunk in a mist and Sango professes her love for Inuyasha, bashing Miroku all the way (and Kagome) and then tries to make out with him.
Sousuke/Insane Police Lady. Sure, they've had some (hilarious) interactions, and the Police Lady is obsessed with him in a Foe Yay-riffic way... and Sousuke did compliment her skill and ability (in his mind). The only problem is that she's only like that with him when he's in his Bonta-kun mascot costume. Which can only say stuff like "Fumo-fumo fuu!!" As for actual interaction between them when he's dressed normally... there's little to none. Except an instance where he asks Kaname if he should "off" the Police Lady.
Foursome pairing of Gauron/Xia Yu Fan/Xia Yu Lan/Sousuke. Not so much the Gauron paired with any of them part, as much as the Yu Fan and Yu Lan together with Sousuke part. Especially since the only interaction he's ever had with either of them was with Yu Fan, whom he never actually saw, and whom he said all of two sentences (consisting of, at most, three words) to. Though, as absurd a pairing as this seems (Sousuke being in a foursome with three people he hates is... not very realistic), it is true that both Yu Fan and Yu Lan had been watching and pondering over Sousuke for a while (since their Sensei kept talking about him, and sent them to find him).
Back in the day, Yamato and Mimi from Digimon Adventure, who have a single bit of interaction in the series aside from standing next to each other. The reason they were such a popular ship was because everyone paired all the characters according to "hierarchy": Taichi and Sora because they were the male and female leads (and because they had actual chemistry), Takeru and Hikari because they were the two youngest, and Yamato and Mimi because... they were the only boy-girl pair left. There were Koshiro and Joe, of course, but they were both really nerdy, and weren't Troubled, but Cute like Yamato. (And yes, this meant that Koshiro and Joe were often paired together - even though either of them would have been a better match for Mimi).
A lot of Digimon Tamers fans who like Ruki/Takato will pair Juri (Takato's canon crush) with Lee or Ryo (both of who're frequently paired with Ruki) despite the fact Juri is rarely seen interacting with them, if ever.
V-mon/Tailmon in Digimon Adventure 02 could also be seen as this. He was shown to crush on her... for about five minutes, and it was never mentioned before or again.
Fullmetal Alchemist has a small fanbase dedicated to Greed/Riza. Who have appeared in the same CHAPTER maybe all of twice.
Trowa/Relena is a decently popular het alternative for Heero/Relena (at least among those who don't want Relena to die in a fire); however, the sum total of their interaction throughout Wing canon is nine lines of dialog, all related to Heero. Such a ship could be seen as Loving a Shadow, since Trowa and Heero are remarkably similar personality-wise, an idea quite a few 3XR fanfics run with.
Wufei/Relena. The two never interact in any form or fashion, not just in the anime or The Movie but in all the official sidestories and sequels. Beyond that, they're polar opposites (he's an Arrogant Kung-Fu Guy, she's an Actual Pacifist), and he makes it plain that he doesn't like her on several occasions. So any pairing would require either Foe Yay of epic proportions, or a serious Ass Pull.
The Ouran High School Host Club fans who keep up with the anime rather than the manga see Kyoya/Kaoru as this, since their time together in the anime is limited to one scene of about 2 lines each. The pairing has developed a niche in the fandom due in part to continuing interactions in the manga.
Someoka/Fubuki seemed to have become extremely popular a long, long time before the two shared any decent amount of screentime, having spent an arc and a half (about 50 episodes) taking turns getting Put on a Bus starting shortly after Fubuki's introduction. In the video games — which the show was based off of — though they have a lot more interaction.
Fudou/Fuyuka, who never interacted in either version, yet it remains the most popular hetero shipping for that character.
Zeref/Mavis, Zeref being the Sealed Evil in a Can and Mavis being Fairy Tail's angelic looking founder. Not only have they never met, but Zeref having no idea Tenroujima was a guild island is as good an indicator as any that he has no idea Mavis exists. No longer the case as of Chapter 340.
Mashima seems to love subverting this trope. Mira/Laxus is a fairly popular crack pairing in the fanndom. However, there has been no sign from either side that could make them a viable pairing until chapter 359. Cue shippers going crazy.
Wendy and Romeo, who haven't interacted at even one section of canon material, and yet fans seem to think the viable reason to pair them up is because Romeo is finally the same age as Wendy.
In A Certain Magical Index, The Hero Touma and the Misaka's Team Normal Saten get paired in a surprising amount in fanfics, despite the fact that they've never even met in canon. Probably because they're both normal (mostly).
Soul Eater has Crona/Death the Kid. Although they only interact twice in the anime and once in the manga, it's a rather popular pairing in the fandom.
In the reboot movie Sulu and Chekov share all of five lines of dialogue. They are still one of the most popular ships in the fandom, and every once in a blue moon will surpass even slash Trope Namer Kirk/Spock on the Kink Meme for sheer number of stories written. Doubtlessly, the ship is helped along by the characters' interactions in Trek Prime canon, but there is a cornucopia of fic set specifically and solely in the Reboot Universe.
Pairing Scotty with Gaila (Kirk's Orion girlfriend) is surprisingly popular. Not only do they share no scenes in the film Gaila is quite possibly dead by the time Scotty even arrives on the Enterprise.
Donny (the Bear Jew) and Utivich don't exchange any lines, but they are one of the fandom's most popular pairings. This can work out though, as the film shows a limited view of the Basterds, and it's possible that they all interacted at some point that we don't see in the movie.
Donny is also paired with Soshanna quite a lot, considering they have entirely different storylines, never meet at all during the film and both die at the end.
The Legion section on Fanfiction.net has a rather large proportion of Gabriel/Audrey, despite the fact that they share precisely one scene, in which she tries to kill him and he does kill her.
Darcy is frequently paired with either Loki or Hawkeye, despite never sharing a single scene with either character. Which is nothing compared to her being frequently shipped with Steve Rogers.
Clint Barton/Phil Coulson.
Howard Stark and Peggy Carter from Captain America: The First Avenger are frequently shipped as having hooked up afterwards to sire Tony Stark. Though they do share the screen a few times, they are usually in group scenes and they share TWO lines of dialogue set about twenty minutes apart and in different countries. (They are friends, though — Peggy is the one who introduces Howard to Steve as 'the best civilian pilot she knows' and Steve thought they were fondue-ing for a good portion of the movie.)
Camp Rock has the pairing of Nate and Caitlyn, which seems to be so for the sole of Caitlyn being straight and not alone. It still goes on even after Nate was given a love interest (and a bigger role) in the second film.
The 2012 film of Les Miserables has given rise to the pairing of Enjolras and Eponine. Although they see each all of three times, and never say a word to each other, a handful of strategically timed back to back shots of each other, a moment where they actually stand next to each other, a significant notice by Enjolras of her entrance into the cafe, and the shot of him sheding a tear as she dies seem to have given the fan enough material for it to become one of the biggest ships in the fandom.
The most popular example might be Draco/Ginny, which was insanely popular for a while and still has a decent sized following, even though they only spoke twice in seven books, way back in Book 2, when Ginny told him "Leave him alone, he didn't want all that!" and later when Draco made fun of her Valentine to Harry. Though apparently the actual actors dated in real life.
Draco/Ginny is also used as a Beta Couple in Harry/Hermione stories, if the writer isn't feelingvindictive. As is Blaise/Ginny, which has even less canon to stand on as, and Blaise called Ginny a "filthy blood traitor".
Sirius Black and Lucius Malfoy didn't exchange a single word in the novels. The sum total of their conversations in the films was "Get away from my godson!" "Black!" There's a pretty solid body of slash devoted to them.
After the fourth book introduced Narcissa Malfoy, there was a rash of fics pairing her with Sirius Black for some reason. Then the fifth book revealed that they were cousins.
The controversial fanfic In This World and the Next has a few examples. Oliver Wood winds up dating Penelope Clearwater after Percy turns evil, though the two are in different houses and are unlikely to have known each other. But that pairing is downright normal compared to some of the other ones that Harry and Hermionecreate. In their zeal to ensure that Remus and Tonks wind up together so that Teddy can be born, Sirius Black ends up having some romantic moments with Charity Burbage. Even more ridiculous is that Neville somehow falls for Millicent Bulstrode, and the feeling is mutual. If For Want of a Nail were not in full effect, the two would most likely have hated each other's guts, assuming that they had any interactions at all.
Jon Snow/Daenerys Targaryen is probably one of the most popular ships in the series, despite living on different continents and that the former has taken a vow of celibacy. It helps that they're probably the closest that the series has to protagonists, and may well be the "Ice" and "Fire" referred to in the title.
The fact that many if not most fans believe that Dany is Jon's aunt only adds to the oddness.
An odder ship is Arya Stark/Edric Storm.
Aegon Targaryen is shipped variously with Dany, Sansa Stark, Arianne Martell, or even Arya Stark or Margaery Tyrell, despite having met none of them.
Sansa Stark/Harrold Hardyng is probably the leading Sansa pairing after Sansa/Sandor Clegane, despite how not only has Sansa not met Harry, neither have the readers. However, a marriage with Harry would give Sansa control of the Vale of Arryn, and a very good chance of reclaiming the North.
Sansa Stark/Jaime Lannister seems to be pretty popular even though the two have barely ever even seen each other, let alone had any interaction, and Jaime's most romantic interactions seem to have been with Cersei and Brienne.
In The Phantom of the Opera fanfiction, Erik/Meg is one of the more popular pairings. In the book he arranges her advancement in the ballet chorus (mostly to ensure the loyalty of her mother), and she finds his mask at the end of the musical, but they never meet and seem to be peripherally aware of each other at best. (Meg does have a thing for him in the musical sequel Love Never Dies, but the lesssaid ofthis, the better.)
Molly Carpenter/Carlos Ramirez is a fairly popular pairing in The Dresden Files fandom. The sum total of their interactions consist of Carlos offering Molly a hand grenade. Though granted Carlos expressed his appreciation of Molly's looks to Harry and goes on about what he'd like to do with her, but Carlos fancies himself a ladies' man and Molly is just that hot.
Within The Hunger Games fandom (particularly with Katniss/Peeta shippers), it's popular to pair Gale with either Madge or Johanna. Although Johanna does (probably in jest) flirt with Gale, it's the only time they're seen together, and he and Madge are also only seen together once by the reader, where he's not half as friendly to her as she is to him. Gale/Madge stems from Katniss jealously wondering if there is more between them than she knows after Madge runs through a snowstorm to bring Gale medicine and Haymitch channels the conclusions their shippers drew from the incident. Gale/Johanna seems to be mostly about similarities in their personalities.
Cato/Clove. They're often seen together, but only as "the District 2 tributes" or as part of the Careers. Admittedly they're from the same district, but the only hint that they're anything more than pragmatic teammates is Cato's uncharacteristically emotional reaction to Clove's death.
In the Penny Parker series, Louise has been paired with Salt, even though they barely know each other.
Sylar and Heidi make for an interesting ship. They've never been seen to meet in the series, but the ship bears a dubiously canon odor due to two timelines in which Sylar murdered and impersonated Heidi's husband.
A lot of fans slash Mohinder Suresh and Adam Monroe, despite having never met. Reasons include Mohinder's status as evil magnet, or the "British connection" stemming from the fanon idea that Mohinder went to boarding school in England... but mainly, the actors are just so freaking pretty.
Claude/Sandra is another popular one. We've never seen them onscreen together, but Claude was HRG's partner at the Company and apparently his close friend, and Sandra is/was HRG's wife, so they most likely knew each other.
The Dawn/Andrew ship, even though they've hardly ever talked and Andrew is in love with Spike. Andrew has expressed a certain fondness for Dawn, and she's practically fawning over him after he refuses to help the First.
There are a fair number of Angel crossovers (probably the majority of them set in season 7/4 in fact) that pair Dawn with Connor, most likely due to their closeness in ages. The two have yet to meet, even in the comics.
A number of fanfics pair Faith and Doyle. To point out the absurdity: Doyle is now dead. When he was alive (for the whole nine episodes) Faith was in a coma, far far away.
Spike/Tara, who traded words maybe once, and Spike/Willow, who had maybe three onscreen conversations over the course of the show (though to be fair, one of those conversations was full of Does This Remind You of Anything?).
Connor/Drusilla showed up occasionally post-Season 4.
In NCIS there is a ship called Kiva - Kate/Ziva. They lived in completely different countries, and never met. And Kate dies before Ziva arrives on the show.
Star Trek: Voyager fandom once had a large sect interested in pairing up minor crew members Joseph Carey and Samantha Wildman, though he only appeared in the first season (and then in a time-traveling fifth season episode) and she wasn't introduced until the second. Though in a crew of about one hundred and fifty people spending several years on the wrong side of the galaxy, it's not unreasonable to assume that everyone has at least met each other. It was a great disappointment to them when Carey was killed in the last season.
Glee fandom seems to ship Jesse with Quinn a lot, despite having only spoken once.
A large contingent of the fandom ships Sam/Gabriel despite the hostile nature of their few canon interactions, presumably because the ship is a good mirror for the Dean/Castiel ship. This is rarely framed as Foe Yay.
The small but growing support for Meg/Castiel (who were on screen together for all of thirty seconds) and Gabriel/Crowley (who never shared a scene).
Mycroft/Lestrade, as illustrated by this video. It wasn't clear that either of them even knew the other existed until mid-series 2, when Sherlock accused Lestrade of being sent to Baskerville by Mycroft (which Lestrade denied).
The ship Moriarty/Moran takes this trope to an extreme - Moran has not even appeared in this show, as of the end of series 2.
From Merlin: Morgana and Sir Leon. Leon was introduced in the second season and had no scenes whatsoever with Morgana in the second or third series, yet it still gained quite a number of followers. This changed in the finale of season three in which Leon is forced to kneel in front of Morgana after she's seized the throne of Camelot. The increase in shippers went up exponentially.
Skins has Cook/Katie, Effy/Emily, James/Paddy, Tony/Cassie, etc. There are even some across the generations, like Tony/Katie and Naomi/Michelle.
In the Tin Man fandom, the most popular Beta Couple to Cain/DG seems to be Glitch and Azkadellia, who meet (as adults) exactly twice in the series—oh, and that bit about her cutting out half his brain and putting it in a jar.
The Grimm fandom features a sizeable fan base for Barry Raeb/Roddy Piper. The two have never met and would most likely be natural enemies (one is a bear, the other is a rat), but they are both Cute but Troubled.
The Vampire Diaries has Elijah & Pearl, and Klaus and Caroline started as this before they started interracting in the show. Anna and Kol could be possible considering their ages, but Anna was dead before Kol appeared in the present.
Many House fans pair Cameron and Thirteen together, even though the two can't have shared more than six or seven scenes in the entire series, and all of those scenes included several other characters.
Downton Abbey's fanbase has a sizeable amount of support for the pairing of Edith with Mary's former suitor Evelyn Napier. They shared only brief scenes, he wasn't very pleasant to her during them, and after his debut in the first series he didn't reappear until the fourth (where he is once again pursuing Mary, Edith is in love with someone else, and the two don't interact.)
Doctor Who's massive universe provides tons of fodder for this. Start with any pairing of a Doctor and a companion that never traveled together (seeing as how the Doctor's on his eleventh incarnation) or two companions who never travelled together. Then there's every other side character ever.
For Stargate Atlantis, there's a decent number of fics pairing together Evan Lorne and Laura Cadman, despite the latter only appearing twice (and spending hardly any time in her own body in the first instance) and being canonically involved with Dr. Beckett. And they never actually meet on-screen (although with the size of the Atlantis expedition, it's more likely than not that they are at least aware of each other)
Red Riding Hood and Archie. In the show's nearly two seasons, they have spoken directly to each other in only one scene, where Archie is ordering something from Red in the diner where she works. Regardless, the pairing has quite a following.
The Mad Hatter and Captain Hook, who have never interacted and were only briefly on the same plane of existence.
Karen/Sidney, both Dark-type specialized Elite Four members. Karen/Will is also pretty popular, and also Karen/Lance and Karen/Grimsley. It's pretty much said that everyone wants Karen.
Cynthia/Steven Stone is mildly popular in the fanbase. They both are/were Champions of their respective regions (Sinnoh and Hoenn) and their signature Mons are pseudo-legendaries (Garchomp and Metagross), and that's it.
Same goes for several couples in later game. In Blazing Sword in particular, ignoring whatever subtext might be present in supports (in addition to, again, Relationship Values), one may have a tough time trying to find out whyHector would want to hook up with Florina, or figuring out whether or not if Matthew’s feelings about Serra really do change for the better, to list some examples.
Any and all Organization XIII shipping in the Kingdom Hearts fandom. It's not so bad for the members who appear in Chain of Memories, but the members in Kingdom Hearts II have essentially no interaction and only appear by themselves. The Director's Cut edition adds a few scenes between them, but all they do is growl about The Plan. 358/2 Days may help with this, provided you're not trying to ship the Castle Oblivion group and don't mind emotionless hatesex. However, it still doesn't explain the absurd popularity of the Zexion/Demyx ship; never in any of the games do the two of them ever interact with one another.
Joshyme (Joshua/Rhyme) is a very popular pairing in the fandom, despite having never met at any point in the game, and are indeed the only two of the five main characters who have never met; everyone else has at least seen each other at one point or another.
Even more popular seems to be Minamimoto/Rhyme. Given that Rhyme is killed off before Minamimoto even comes anywhere near the rest of the protagonists, this is slightly mystifying.
In the Professor Layton fandom, there's pairings such as Flora/Clive and Descole/Emmy. They're both fairly popular, although the characters don't really interact all that much. There's also a few with Layton, although he's a Launcher of a Thousand Ships.
Ace Attorney fandom has quite a few, but one that sticks out is Mike Meekins and Maggey Byrde, while on the villainous side we have Dahlia Hawthorne and Kristoph Gavin.
The vast majority of the extensiveTouhou cast have never interacted or shown evidence of being aware of each other, due to being a Shoot 'em Up, and even in the Expanded Universe most characters rarely stray from their Cast Herd. Thus, almost all possible ships are like this, with basis for a pairing being anything from appearing in adjacent stages, to bad jokes (e.g. shipping the bug girl with the plant lady). Gensokyo is at least confined and not a large place, so everyone ought to run into everyone else eventually.
The website Legacy of Kain fansite Bleeding Beauty, devoted to the character Umah from Blood Omen 2, makes a case for Umah/Magnus, two characters that never meet in the game (after considering pairing her with every other character in the game).
Theoretically, shipping almost any party member with anyone butShepard will result in this. This effectively means that Garrus/Tali is exactly as possible as Grunt/Jacob, which in turn is as likely as Legion/Mordin or any combination of the above. This gains a certain hilarity in Mass Effect 3 where if Shepard didn't romance either, Garrus and Tali hook up at the end of the game.
Party members, at least, can be chosen to go on missions together - at the very least, they serve together on a ship with a very small crew. More difficult to justify is the surprisingly popular pairing of Oriana/Kolyat - relatives of different party members, who never interact with each other, barely interact with the player character, and live on different planets, and seem to be paired up largely due to being the only teenagers in the game.
Shadow and Amy is astonishingly popular considering how little the two interact. It helps that one of their two interactions in Sonic Adventure 2 is the crux of Shadow's Heel-Face Turn, because Amy reminds Shadow of his dead best friend, Maria Robotnik.
There's quite a few Shadow/Tikal shippers, despite the two never meeting, and the latter's unfortunate handicap of being dead.
Silver and Blaze could be considered one. The game it originated from was erased from canon, and the two have had very little canonical interaction.
Kirby's Return to Dream Land: Due to their common jester-like appearances, Manipulative Bastard tendencies, and similarities in general, Magolor is commonly paired with Marx in fanworks, but there is little to no evidence that the two have ever met, save for one line that he says on board his ship, stating that he heard about Kirby "from a friend".
Dishonored has Daud and TeagueMartin, who have never met in-game. Also, Martin is dead by the end of the game and Daud could be dead, depending on the player's choices. Quite a few people ship them anyway.
Portal fandom has the Space core and Curiosity core, even though the Curiosity core was introduced, and dies, in the first game while the Space core was introduced and shot into space in Portal 2.
Abe and Kroenen centers around Abe Sapien and Karl Reprecht Kroenen, two characters from Hellboy getting together in a secret post-film romance, even though they never shared a scene.
Ask That Guy and The Nostalgia Critic. While its pretty easy to see Ask That Guy wanting to bang someone who looks exactly like him, the characters have exchanged like five lines of dialog. But suddenly in fanfic, they're incestuous twins who are ridiculously co-dependent and the Critic is usually Ask That Guy's fuck-and-torture toy.
As soon as Dr. Tease's evilness became apparent, people started shipping her with Dr. Insano.
Flippy/Splendid has a surprising following, especially in the Japanese fandom, in spite of having never met. One of the reasons may be that people always wanted them to fight each other, so that they could see who would win, which earned them a lot of popularity. In Japan, it is probably the most popular pairing after Flippy/Flaky and Handy/Petunia.
Nutty/Flaky is strangely popular, even though they've only interacted on screen once and that was when Nutty was a total douche to her.
Pop/Disco Bear, even though they're polar opposites in personalities.
Toph/the Duke and Toph/Teo are popular Ship Mates for the canon pairings. The former's sole interaction is Duke letting Toph use his helmet as a barf bag during "The Day of Black Sun", and a hug in the finale (during the finale commentary, the creators coyly point out the hug). There's hardly any at all for the latter.
Ursa, meet Hakoda, Hakoda, meet Ursa, I think you'll get along great. Oh yeah, we ship Ursoda. Theme Pairing: opposite-gender single parents of two major characters each. Pulled off exceptionally well here.
Azula and Toph are starting to gain a small fanbase. The two only talk once, in "The Day of the Black Sun", when Azula proves she can get past Toph's Living Lie Detector ability.
After being asked "Who is Lin's father?" one too many times, one of the writers decided that it's Azula.◊
Some Zutarians like to ship off Mai with Jet, despite Jet being dead and they've never met.
Believe it or not some Jet/Azula fics exist. Not only have they never met but, given their respective personalities and loyalties, they would almost certainly try to kill each other on sight should they ever do so.
The Zutara (Zuko/Katara) ship started out this way. Yes, they ran into each other half a dozen times in the first season, but with the exception of one scene where Zuko tried to barter Katara's necklace for Aang, he never even spoke to her. The second season was even worse. It wasn't until the season finale that Zuko and Katara had any real interaction with each other, but the Zutara ship was already running strong.
June/Piandao is another one that's appeared.
Haru/Ty Lee were paired in the Super Deformed Shorts, despite never meeting.
There's a surprising amount of Jinora/Skoochy fic. One is Tenzin's Cute Bookworm airbender daughter and the other's a street rat who trades information for money, and naturally they've never met; they just happen to be the only ones in their age group.
Bolin and Lin is semi-popular ship too, in a Pair the Spares kind of way, despite of the age difference. They are in a lot of crowd scenes together, but their only interaction with each other is the time Lin busts Bolin and Mako out of jail. However, in that scene Lin zips up Bolin's fly for him, which caused all manner of reactions form the internet.
Robin/Raven used to be this way. Of all the Titans, they interacted the least, yet people liked pairing them up because they liked the aesthetics of it: both were the darkest Titans, both were named after birds so writers could do a contrived "birds of a feather" metaphor, etc. It wasn't until the Trigon Story Arc where Raven started confiding in Robin more and scenes like Robin rescuing a mindraped and clothing-torn Raven that shippers finally had decent canon stuff to write off of.
Blackfire and Red X. Never met, but each is the Evil Counterpart to the official couple of Robin and Starfire.
Even more extreme is Slarella - Slade and Arella. One is an enemy of the Titans living in their dimensions, and the other is the mother of a Titan living in an alternate dimension.
Craig/Tweek is the most popular crack pairing and the most popular pairing after Stan/Kyle and Cartman/Kyle, even though they have directly interacted only in one episode.
Damien/Pip. The two only appeared in an episode together, for a few moments, during Damien bullied Pip and set him on fire.
There's more than a few shippers for Stan and Ike, despite the interaction between the two being nothing more than Ike being the little brother of Stan's best friend.
Kenny/Butters is surprisingly popular; while you do see them hanging around each other quite a bit, they don't actually interact - Kenny interacts a lot more with Kyle, and Butters with Cartman. The two did eventually get screentime together during "Going Native", which only fueled their fandom more.
A fair number of people pair Stan's sister Shelley and Kenny's brother Kevin, most likely because they appear to be around the same age, have braces, and are older siblings of two of the main boys. These characters have had literally zero interaction and the number of spoken lines Kevin has had during 16 seasons can be counted on one hand.
Total Drama crack fans will pair just about anyone together, so there are several popular examples of this: Izzy/Ezekiel, Noah/Katie, DJ/Eva, Tyler/Gwen, Cody/Bridgette, Cody/Sadie and DJ/Sierra, all of which have had little to no on-screen interactions.
Trent and Courtney are a popular fanon couple despite barely interacting in canon (in fact Trent may be the contestant Courtney has talked to least on the whole show), usually as Ship Mates for people who want to see Gwen and Duncan together.
Phineas and Ferb has Ferb & Gretchen (the Fireside Girl who wears glasses). Despite Ferb's Precocious Crush on Vanessa and their lack of onscreen interaction, it's a very popular ship.
Just try to tell some of the Wolverine and the X-Men fans that Forge and Toad have never so much as been in the same room together. That doesn't stop them from being rather plausible if they ever did meet, or the fact that their ship is hands-down the cutest one in the fandom.
Prowl and Blackarachnia only met once and all she did was poison him so she could manipulate Optimus. But his Friend to All Living Things and her self-loathing for her technorganic Body Horror had a strange appeal for fans.
A very extreme, disturbing example is a fanart involving Blurr/Longarm, despite the only interaction they ever had was when the former was killed by the latter.
Transformers Prime has Knock-out and Arcee. The two of them barely spoken and have little interaction with each other, and the little they have is hostile. Yet this seems to be the fan favorite pairing if fanfiction has anything to say about it.
Dib/Gretchen is an odd example. They only interact in about two episodes, and in one of them Gretchen doesn't even speak. However, that silent appearance makes it very clear that she has a crush on him. It comes nowhere near Zim/Dib or Dib/Tak in popularity, but the ship has its supporters for being the most "normal" and only real canon couple on the show.
Daria has a few examples—some fans ship Ted with Stacy, for example, based on their similarly kind and intelligent personalities. Mr. DeMartino and Ms. Defoe, the most notable teachers to still be single at the end of the series, are also sometimes paired together.
Due to the Improbably Female Cast, opposite sex pairings that don't involve Big Macintosh are very prone to this. Soarin'/Applejack is one of the more plausible ones (he bought a pie from her, and that's it), while ones like Twilight Sparkle/Doctor Hooves and Pinkie Pie/Pokey Pierce are not uncommon.
An especially odd example (if only because of how popular it is) is the shipping between DJ Pon-3/Vinyl Scratch and Octavia. It started with fans juxtaposing the two forhumorouseffect since they represent conflicting musical aesthetics. However, the sheer volume of such fan works was enough to get the gears turning for the community's shippers, to the point that a large chunk of fan art, fiction, comics, etc. involving the two is now shipping-based. DJ Pon-3 also has a growing Shipdom with Neon Lights/EmCee W1SH, who in popular fanon is seen as another musician who has a friendly rivalry with her. It should be noted that DJ Pon-3 has yet to appear in the same scene as either of her two most popular shipmates, only appearing in the same episode as Neon Lights in the Season 2 finale and only appearing with Octavia in The Merch.
Invoked in "Heart's and Hooves Day", in which the Cutie Mark Crusaders try and pair up Big Macintosh (of course) and Cheerilee, two ponies who before this episode never even stood next to each other. It goes about as well as expected.
In X-Men: Evolution fandom, Pietro/X-23 and Kurt/X-23 are very popular ships. her and Kurt's closest interaction being off screen and involving her knocking him out, and her and Pietro's closest interaction only happening in people's imaginations. Kitty and Pietro is slightly more believable, but even more jarring as the two have interacted, and by 'interacted' we mean Pietro insults her, she glares at him, and once threatens him.
Recess fans tend to ship Hustler Kid and Butch, who hardly interact in the series.
Young Justice: "Wonder Beetle" (Wonder Girl/Blue Beetle) is a surprisingly popular ship, seeing as the two characters have yet to exchange any dialogue on the show. The tie-in comics though have the Scarab note that seeing Wonder Girl causes "bio-chemical changes" to him.
The Scar/Sarafina (Nala's mom) pairing in The Lion King fandom. The latter is such a minor character that her name isn't even revealed until the credits role, they are at most in two scenes together (although you have to really search to find her), and never once do they interact, yet after Zira, Sarafina's the most popular character to pair up with Scar. The main reason this pairing exists is to answer who Nala's father is.
CJ/Thomas from Regular Show. They've never met; CJ only appeared once and Thomas didn't debut until after that.
Alexis Denisof (who played Wesley on Buffy the Vampire Slayer and Angel) married Alyson Hannigan, who played Willow on those shows. The two characters barely spoke to each other within the show, so this is perhaps a real life example of something like this happening!
They started dating after Denisof's move to the spinoff show Angel, in which Hannigan has appeared in only three episodes. As a guest star. One of those appearances count as the only time Wesley and Willow have ever had a canon conversation.
Amber Benson, who played Tara, and Adam Busch, who played Warren, have been dating for nearly a decade. They only interacted together once on the show, and even that was more Warren's bullet interacting with Tara's chest.
The above also happened with Mariska Hargitay and Peter Hermann of Law & Order: Special Victims Unit, the former of whom is Olivia Benson, and the latter of whom is the recurring defense attorney Trevor Langan. Hargitay and Hermann are married in real life, but they barely speak to each other on the show. Hilariously, Langan was a temporary love interest for ADA Alexandra Cabot.
On The Vampire Diaries, there was a relationship between Candice Accola (Caroline) and Steven Mcqueen (Jeremy). The characters rarely ever spoke.
Also Paul Wesley's wife Torrey Devitto joined the cast in Season 3. The two didn't share a scene until the next season.
Michael Douglas met wife Catherine Zeta-Jones during the production of Traffic, a film where they never share a scene.