As a series progresses, it has a lot of events in it which are supposed to be happening for the first time. Once you do more of the series, you can have characters who have met before meet again, or you can revisit old locations or plots, or whatever.
But if you're doing a prequel, the temptation is to write the same way, by using elements of the series that are familiar to you and your audience. This means using varying degrees of Retcon to say that the "first" appearance of someone or something wasn't really the first, so that you can use it in the prequel. In extreme cases this can lead to a Continuity Snarl where most of a story's cast, antagonists, abilities, etc. all showed up before the main story even began.
Sometimes the pre-first first appearance gets explained away by giving characters amnesia or otherwise effectively wiping out the event, which can itself get weird if it happens lots of times.
A variation may be seen when Time Travel gets involved, and characters meet people in the past who aren't supposed to know them until later. This can be solved either by Laser-Guided Amnesia, or by having the other characters not recognize the time traveler (because he/she either has changed his/her appearance or meets them so far in the past that they've forgotten it by the time they meet in the present).
See also Spinoff Babies, Everyone Went to School Together, Everyone Is Related, Early-Bird Cameo, Forgotten First Meeting, and Connected All Along.
Anime and Manga
The 2002 television special Lupin III Episode 0 First Contact tells the story of how all the main characters met, all at the same time. This contradicts previous origin stories that showed Lupin and Jigen being old friends, then meeting Fujiko, and then meeting Goemon much later. However, the whole thing is told through the Framing Device of Jigen being interviewed by a news reporter, and it's never confirmed that the events of the movie really happened. Especially as a second Jigen shows up to reveal that the first Jigen is actually Lupin in disguise, and probably lying about everything.
Apart from Lupin producing the MacGuffin of the movie during the epilogue/(credits roll).
Back in the Silver Age, the Superboy series pioneered this, with just about everything from Superman showing up "first" in Superboy, including Lex Luthor being a former childhood frenemy.
It also provided at least one serviceable subversion, creating Lana Lang to stand in for Lois Lane rather than importing Lois into his childhood. She even became fleshed out into her own character. Pete Ross arguably was a stand in for Jimmy Olsen and even he took on his own life (being Superboy's first Secret Keeper aside from his parents, both from an in-continuity and real world perspective.) Although in the end, Superboy met both Teenage Lois and Infant Jimmy anyway.
It reaches really ridiculous levels in the standalone graphic novel Superman: Blood of My Ancestors, where we learn that that Kal-El wasn't even the first person in his family to become a super-powered crusader. Apparently, in Krypton's distant past, Kal-El's ancestor "El" developed suspiciously Superman-like powers after dying and being resurrected by the god Rao, going on to become a revered messiah (complete with a rudimentary "S" symbol painted on his chest) and fight an evil bald warlord named "Utor" before being brought down by his weakness to Kryptonite. So...even though Superman's powers are supposed to come from exposure to Earth's sun, they really just run in the family.
This sort of silliness isn't confined to the Silver Age, either. One Modern Age story in World's Finest shows Jor-El scouting out possible planets to rocket baby Kal off to with a sort of ultra-3D Subspace Ansible. Which lucky Earthling does he chat with to see if the human race might be up to the task of raising the Last Son of Krypton? Why, Thomas Wayne, of course.
As the G.I. Joe comics progressed, it ended up that Snake-Eyes had met practically everyone else in the franchise prior to joining the Joes, from fellow Joes Stalker and General Hawk to the villains Cobra Commander (whose brother was responsible for the death of his family), Destro, Baroness and Storm Shadow.
Apocalypse from X-Men was later revealed to have encountered, over the course of his long life, the following characters from different corners of the Marvel Universe: Mister Sinister, Externals, Avengers villain Kang The Conqueror, the Brood, Acient Avatar of Khonshu, Abraham van Helsing, Jonathan Harker and Dracula.
In the movie Young Sherlock Holmes, not only do Holmes and Watson know each other in boarding school as young teens rather than meeting as adults as happens in the books, but in a short post-credits scene it's revealed that Moriarty's enmity towards Sherlock Holmes goes much further back than the books indicate: he was a junior master at the school that both Holmes and Watson went to, and the mastermind of the first case Holmes ever solved. Lestrade also plays a part.
The writer also interestingly makes Holmes and Watson the same age. From internal evidence in other stories in the Holmes canon, Holmes in A Study in Scarlet is 27 and Watson 31, so not likely to be bunkmates.
Lampshaded during the credits, where the fimmakers admit the whole thing was a "what if?" scenario
C-3PO had his memory wiped at the end of Episode three. Necessary, because it explains the otherwise awkward complete lack of scenes in A New Hope where C-3PO says something along the lines of "Skywalker and Kenobi, huh? You know, it's funny ..." We can kind of explain Obi-Wan not recognizing the droids as a case of "You all look alike to me." It's perhaps a bit odder that he doesn't recognize them even after learning their names, but R2-D2 is referred to several times as "an R2 unit" as if it were a model number, so apparently his "name" is just "D2" (presumably a shortened version of some longer serial number). There are only about 1300 possible two alphanumeric character combinations so it's likely there are a lot of R2-D2s rolling about the galaxy.
Fanon has it that Obi-Wan knew well who the droids were, but was keeping quiet because he and R2-D2 both agreed that Luke wasn't ready to know the truth about Vader yet. This later became (partially) Ascended Fanon when Luke found out R2 had video recordings of his mother's death at Vader's hands.
According to the Pokémon 4Ever movie, Professor Oak first met Ash, Misty, Brock AND Team Rocket 40 years previously when Oak was brought forward in time by Celebi. Of course, none of the main cast make the connection due to age differences. But you'd think he would have mentioned it at some point.
They knew Young!Oak by first name (Sam), and his notebook's similarity to the Pokédex is commented on. However, given the time travel thing, you'd think the penny would drop after Oak mentions Sam's name before Ash mentions it.
4Kids actually went out of their way to make it completely and utterly obvious that Professor Oak = Sammy, to the point where there were extra scenes added solely for the dub. The original was much more subtle in that it was basically one scene during the credits, specially the scene where Tracy pulls out Oak's sketch book and sees the drawing Sam was doing earlier in the film.
Downplayed to the point of being Played for Laughs in X-Men: First Class: turns out Magneto and Xavier met Wolverine decades before the first movie... but their meeting was so brief ("Go fuck yourselves.") that none of them remember it (and Wolverine wouldn't remember it anyway because of his amnesia).
In Days of Future Past, however, Xavier does remember Wolverine (if Magneto does too, he shows no sign of it).
Dragonlance is like this. You have the Chronicles, then the Twins trilogy, and then they start filling in every character's backstory, usually featuring one or more characters from the chronologically later canon. Considering that the characters were supposedly no more than fourth level or so when they started the 1st Edition AD&D module, Dragons of Hope, the likelihood of them having that many glamorous adventures together is... pretty small.
Artemis Fowl did the Time Travel version in The Time Paradox. Artemis and Holly go back in time and meet a past Artemis and Butler. The past versions eventually have their memories wiped, but it's implied that Artemis' residual memories of the meeting spark his interest in fairies, leading to the events of the first book.
This happens quite a bit in the Redwall book series, both for the characters and for the history of Mossflower, Salamandastron, and the Abbey itself. There's eight books set chronologically before the first one that was published, which leads to quite the bit of Continuity Snarl. This might explain Jacques' later focus on books set after Redwall chronologically, as it gave him more room to work with.
The worst offender is Martin the Warrior, an entire book is devoted to Martin's adventures before he came to Mossflower, despite the fact it had already been firmly established what his backstory was. The Legend of Luke turned this Up to Eleven as a single one paragraph story of what happened to Martin's father became an entire Shoot The Shaggy Dog Story.
Archer also encountered the Borg nearly two centuries before Star Trek: The Next Generation. The writers had to take great pains try to show why none of this knowledge would survive into the TNG era when it would have been extremely useful.
Although that being said, it does lay to rest a minor Fridge Logic issue about a) how Starfleet could have a "foremost expert on the Borg", who they've only encountered the once, and b) why said expert is a character we've never seen before and who wasn't on the Enterprise-D when they first encountered them.
Ditto for the Ferengi. The name itself is uttered early in the first season, but even T'Pol hasn't heard of them at that point. Later, a group of them hijack the Enterprise... but they never once name their species, and no one thinks to ask. All of this is seemingly designed to maintain the continuity.
Babylon 5: The prequel TV movie establishes that John Sheridan had already met and been on a mission with Dr Stephen Franklin during the Minbari War, some twelve or thirteen years before Sheridan became Franklin's commanding officer. Admittedly a very mild example—it's not that far-fetched for an officer and a medic to meet during the Gulf War and then have the officer, now a colonel, assume command of the medic's unit during the Iraq War.
It becomes less mild when you consider that G'Kar was also with them on the mission, that they got bombed on Londo's orders, and that as a result they were captured and met Delenn.
Somewhat justifiable that Sheridan and Franklin didn't recognise Delenn, since they weren't in the best condition at the time, and Delenn looked very different when Sheridan met her again, and Londo had good reason to keep his mouth shut, but you'd expect Delenn to make some reference to it, and you'd expect Sheridan to recognise G'Kar.
It becomes even less mild when you consider that the only thing saving Franklin's (and Sheridan's) life was the Minbari word Isil'zha (i.e. "the future"). One would assume this word's burned into one's mind for the rest of his life. When Marcus showed Franklin the ranger badge, Franklin had seemingly never heard the word.
Happened a lot on Friends, thanks to the various flashback episodes the show featured during its ten year run. Notiecably Chandler was originally just Monica's neighbour but early on the writers expanded on this so he was Ross's college roomate, met Monica and Rachel while they were in high school and spent frequent Thanksgivings with the Gellers, to the extent that he was the cause of Monica's weight loss and she contributed to his hatred of Thanksgiving. The writers stated that he became Monica's neighbour because, now as close friends, she tipped him off about the avaliable apartment across from her.
Tripped over in Sledge Hammer!. Since the first season ended with everyone dying in a nuclear fireball, the second season was a prequel to the first season — despite the fact that the main characters met in the first episode, and weren't partners before.
An alternative interpretation is that there was a 5 year gap between the penultimate and final episodes of the first season, and season 2 fitted in there. This seems to be what the 'disclaimer' at the start of season 2 is implying.
Community established in "Foosball and Nocturnal Vigilantism" that Jeffrey and Shirley met for the first time when they were 12 - but it wasn't until this episode that they realized it. While it was a very memorable experience, it was also very traumatic for both of them and resulted in major personality shifts for both of them. In effect they are very different people than when they briefly met as kids.
The episode "Heroic Origins" crosses this trope with One Degree of Separation. Turns out Jeff briefly met Britta while he was still a lawyer, Troy threw some paper at Abed while they were both in the same frozen yogurt place, etc.
Coupling did this in the episode "Remember This", which had flashbacks to a party several years ago that all the main characters attended before they'd all met one another and become friends. The point was to backdate the Unresolved Sexual Tension of Beta Couple Patrick and Sally, whose relationship had been simmering for two series already.
Leverage did an episode of this in "The Rashomon Job."
Wicked. Prior to The Wizard of Oz, the witch Elphaba knows Glinda, met the Cowardly Lion, in the musical knows the Scarecrow and Tin Man, and of course her father is the wizard who she also has met.
In the second season of Telltale's Sam & Max: Freelance Police games, it's revealed that Sam built Bluster Blaster, an arcade game he met earlier in the series and showed no signs of recognising, when he was a preteen.note Given the nature of the games, this is almost certainly a parody of Star Wars Sam and Max lampshade this:
Max: Funny, though. All this time we've spent talking to the COPS, and you never once mentioned you're the guy who built Bluster Blaster. Sam: Just never seemed relevant, I guess.
Averted in Professor Layton and the Last Specter. It's the fourth game in the series, but set first in the timeline. However, it still features appearances by Granny Riddleton, Inspector Chelmy and Barton, who chronologically first meet the Professor later. To avoid plotholes, the Professor and Luke never cross paths with them, only Emmy does (she never appeared in the earlier games). In fact, Granny Riddleton quickly goes on vacation and leaves her cat behind to perform her usual job, so the Professor never sees her. In Miracle Mask, Granny appears, and even meets the Professor, but she disguises herself and uses a pseudonym for no apparent reason, and in all other occasions when she appears she pretends not to know the heroes, so canon is preserved nonetheless.
Metal Gear Solid managed to retroactively pull this. The prequel Metal Gear Solid 3: Snake Eater almost completely averted it, with Ocelot and Big Boss as the only characters from later in the timeline to show up. Metal Gear Solid 4: Guns of the Patriots, however, retconned it so everyone of importance from all the games (including 3) turned out to be deeply involved in the Gambit Pileup. SIGINT and Para-Medic were actually DARPA Chief Donald Anderson and Dr. Clarke, respectively, and both of them were founding members of the Patriots alongside Big Boss.note Metal Gear Solid 4 was intended to be a Grand Finale, tying up every single loose end that could conceivably be found.
Parodied in PvP when the main characters were brought back in time by a magical d20 and stumbled across Skull. When they get back, they ask him why he never mentioned meeting them before. He says he "used to drink a lot back then".
Notably averted by The Order of the Stick, despite being a continuity-heavy series that actually has fairly important prequels.
The prequel Start of Darkness (the story is the trope namer for eponymous trope) almost exclusively follows Big Bad Xykon and his Dragon Redcloak, during which time they do not interact with any characters who weren't, at best, Posthumous Characters in the main comic. Mostly it shows characters who never appeared and will likely never appear in the online comic that influenced the lives of Xykon and Redcloak. The closest anyone gets to interacting with any members of the main or supporting cast is when Eugene Greenhilt (father of the comic's main character) walks in on Xykon dueling and killing his mentor, (which had been mentioned in the comic) and Redcloak's brother Right-Eye trying to help Eugene kill Xykon so that Right-Eye can escape being Trapped In Villainy.
The other prequel, On the Origin of PCs, focusing on the heroes, doesn't have characters meeting before what was established in the main plotline as their first meetings: Roy and Durkon were friends before the Order formed, but the others only met them and each other right before the main events of the comic.
The Hercules TV series has Herc being quite the hero, even though much later, in the movie, he admits he's never done anything heroic to the disenchanted citizens of Thebes. He spent far more time causing accidents, and never went to Thebes in the series (usually in Athens, but went almost everywhere else in or near Greece besides Thebes). There's the fact that up until his reappearance as an adult in the movie, Hades didn't even know he existed, in fact he thought he had been killed as a baby.
At the very least though, in the one episode Megara appeared, they hurriedly had both she and Hercules lose memory of each other so that they could meet again in the movie.
Spoofed repeatedly on Futurama, which features Scruffy the Janitor, a fellow who meets the cast for the first time... every time he appears. Whenever Scruffy enters a scene, there's usually a mention of how he has no idea who any of the main characters are, and none of them know who he is, either, thus deliberately contradicting all his prior appearances. This leads to such lines as "Gee, I've never seen Bender so upset... or ever before."
The second movie plays with the spoof when it reveals that Fry has both Scruffy's home and cell phone numbers on his speed dial.
A The Simpsons flashback episode showed that Homer and Marge had briefly met and shared their first kiss as children, but due to Marge's straight brown hair and Homer'sElvis Jagger Abdul-Jabbar's patch over an injured eye, didn't recognize each other when they attended high school together.
One flashback episode shows Homer meeting Ned Flanders while Marge was pregnant with Lisa. A later flashback episode shows Homer and Marge meeting Ned and Maude while both couples were childless.
As with Futurama, spoofed in the early years with Mr. Burns. In his very first appearance, he tells Homer, "Ah, Simpson, at last we meet." Was true at the time, but a couple of later flashback episodes showed that he had already met Homer twice before at least. Of course, this was all part of a then-Running Gag that Burns could never remember who Homer was and had to be corrected.
Burns: Smithers, who is this man? Smithers: Homer Simpson, sir; one of your drones from Sector 7G. Burns: Simpson, eh?