Sometimes, due to the nature of the medium, it's hard to spot moments in manga or anime that just seem to come out of left field.
In the 1980s episode of Astro Boy "Uran's Twin", Uran and her double suddenly go into a song and dance about who is the real Uran. The song is never mentioned again afterwards and is not even in the dubbed version.
Arashino Yoru Ni has this random female wolf with white fur just show up there for no reason and having nothing to do with the film's plot. Once she disappears, she's neither seen, heard, nor mentioned again.
Axis Powers Hetalia's 18th episode. The Axis and Allies are fighting, and the giant Godzilla-sized embodiment of Roma Antiqua just rose from the...sea...and... just watch...
Although this one is mentioned again in episode 32, by Roma Antiqua himself to Germany.
How could we forget the mochi strips? I don't know how those were handled in the anime, but in the webcomic, the aliens really sum it up best: "O god...wtf?" This is for a good reason.
Paint it, White! has several, even if one does not count the random recycling of clips from other episodes:
Prussia tries to hold a talent show and have Ukraine and Belarus sing "Carrot and a Stick", which flops when they cancel at the last minute. Apparently the Japanese version vaguely connects this to the plot by having the show be canceled because of the alien invasion, but it doesn't affect the plot at all. In the English dub, not even that connection is made.
Austria is asked by Japan to write music for the Bon Dancing Festival, which he feels he is unable to do. Not only does the scene come out of nowhere, but Japan has already held the festival by this point and apparently had no problems with the music. It might be a flashback, but it still is never referenced again.
In the middle of the final fight where most of the Nations are turned into Pictonians, the movie cuts to a scene where Chibitalia and Holy Roman Empire are standing in a field, saying each other's names repeatedly. It immediately cuts back to the fight.
At the climax of the movie, Rome shows up in a Kiss-like costume, performing a rock version of "Heaven and Hell". While the scene does have some effect on the story (he uses this opportunity to distract the aliens from Italy, and leave Italy a magic marker to fight them), everyone pretty quickly forgets that the personification of Ancient Rome gave a rock concert.
Azumanga Daioh certainly seems to be full of Big Lipped Alligator Moments, too many to list, but among which include "one life one meeting", the new year's dream sequences, and the kitchen knife incident with Osaka, particularly in the anime when it cuts to Tomo splattering ketchup onto some eggs. But then again, many fans consider the presence of these Big Lipped Alligator Moments part of the show's charm.
At one point in the manga Beelzebub, a side panel is used to explain a slightly obscure term one of the characters uses. This explanation is placed over an image of a teddy bear at a bar, with a footnote saying "This picture has no relevance what-so-ever."
Kuma-chan strikes again later on, for absolutely no reason this time, when instead if sitting at a bar it's taking a bubble bath.
Bobobo-bo Bo-bobo: being a series that is nothing but BLAMs, one stands out in particular, where Beauty, the Only sane man of the group, suddenly snaps and begins playing along with the wierdness for no reason, once Bobobo and Don patch get back on screen and do something strange, she's right back to normal, no explanation given, no comments made.
There is an early episode of Digimon Adventure 02 that, although comedy-driven and not supposed to be taken seriously, has a pretty jarring scene. Simply putting, V-Mon all of a sudden admits having romantic feelings for Tailmon and decides to train hard to evolve and impress her. It's a very strange scene, mainly because in the Digimon series (especially the Adventure continuity) almost no Digimon ever show romantic affection for other species of Digimon. And of course, this affection was never even hinted before, and it's never mentioned later.
That's only a semi-Moment. The event indirectly leads to V-mon evolving for the first time — and even though it's not mentioned in the actual series, the fans tend to have issues...
Even more so is the episode "Dagomon's Call". While the V-mon evolution episode fits the tone of the series' more comedic moments, this episode suddenly and with no apparent reason shifts into a dark, Lovecraftian story where Hikari is targeted by an (apparently?) evil being; gets depressed, sick, and a little neurotic; and is spirited away to an alternate dimension (which may or may not be different than the one they're usually going to), where she might have been stuck if her friends hadn't come to find her. It's especially jarring since the tone of the story does a complete 180, suddenly using minimal dialogue and few sound effects in a way that completely clashed with the show's overall tone. The most that's ever mentioned again is the recurring (and never entirely explained) Dark Ocean setting.
The Dark Ocean storyline visited in the episode was originally planned to see expansion, but this was scrapped due to meddling from Bandai and disputes amongst the writing staff.
The only time the Dark Ocean is mentioned again is when Daemon is sealed in it. Speaking of Daemon, he's another example. He's extremely powerful villain that has no connection to the events of the main story shows up with no explanation for what he is or where he came from that nearly decimates the protagonists, and isn't mentioned again.
Also in Digimon Tamers, which is much more serious than its predecessors, there was this bizarre scene with a talking owl. What it said was important to the plot, but it is never revealed why it could talk, or why it spoke like a preacher, or how it even knew what it knew. The owls words are recounted, but no one ponders why it talks, or where it got its knowledge. It is very bizarre compared to the overall tone of the show. Here is a link to it http://www.youtube.com/watch?v=8fDdK1T_oDM
The third episode of Adventure 01 opens with the protagonists getting caught between two Monochromon, thinking they're trapped. The Monochromon proceed to fight each other, leaving the protagonists free to leave. It has nothing whatsoever to do with the episode's plot and isn't mentioned again.
In the first Dragon Ball Z movie The Dead Zone, Gohan eats a magic apple, which causes inebriation in children. Cue musical sequence with dancing dinosaur hallucinations. The next movie has another spontaneous Gohan song, and while the lyrics and visuals are just as trippy, this one doesn't even have a magic apple to justify it.
In an episode of Z, while he's training with Piccolo, Gohan falls down a cliff, tries and fails to get back up...and then starts shouting out Shiratori words. Notably, each and every English dub of this scene has that moment completely rewritten, presumably because of how nonsensical it is.
Vegeta's desire to take over the Earth and fighting with Gohan after finding out that both Goku and Freeza had (apparently) died. It's a complete non-sequitur (it's anime-only filler that doesn't occur in the manga), it's odd considering that Vegeta later said that he actually wants to see Goku alive and it's never mentioned again, Gohan is seen in the next episode uninjured and Vegeta, who flew off, is standing exactly where he was in the previous episode, also uninjured.
The wing scene in Eden of the East. It's rationalized, somewhat, but the fact that it is so fuck-outta-nowhere in a political thriller, you'd think the characters would be shaking their heads in disbelief for at least an episode. Though given the amount of hallucinogens they just inhaled, they may be forgiven for it.
There's also the scene where Akira nearly drives his bike off an unfinished bridge for no apparent reason, and has a bizarre hallucination of a bunch of creepy white zombie things which lick him while he laughs and calls them Johnny. Then they start biting him, so he yells at them, and suddenly the hallucination ends; Akira drives off as if nothing happened. It's probably some kind of weird metaphor for how he saved everyone on Careless Monday, but in any case, the whole waking dream is treated like a pointless diversion and is never brought up again.
Pretty much all of Fuuko Ibuki's appearances after her initial arc in the first season count as this, mostly because all of the main characters don't remember her. This is mainly due to the fact that she's the Astral Projection of a girl who's in a coma, but that doesn't make them any less hilariousnor more, or any less random.
As pointed out by the guys at Deconstructing Comics, in the original Ghost in the Shell manga the plot is abruptly interrupted by several pages of a cyberspace lesbian threesome that ends with an abrupt cut back the participants in the real world where they are on separate beds and couches, and fully clothed. This is not only never brought up again, but the rest of the manga is fairly prudish compared to Shirow's later work. Besides being basically several pages of porn in an era when manga was still a new art form in the US and seen as a kid's medium, it was seen as pointless enough that most early editions of the book left it out completely (besides the fact that it would have never gotten past the censors).
In the Ghost in the Shell Stand Alone Complex episode "Not Equal", Batou and Saito decide on a course of action and start running through a slummy market and they run past two people dressed as teddy bears being led along on a leash by a man holding a sign with a heart on it.
Heavy Object has an almost perfect example. During a firefight between the protagonists and the enemies in Antarctica, a baby penguin wanders into the battlefield. Both groups stop shooting at the exact same time, to avoid harming it, and they start to silently cheer for the penguin. Then, an albatross appears and tries to attack the penguin, but the penguin's mother appears and engages in a staredown to protect her baby. Eventually, the albatross gives up. Both groups cheer loudly, shoot into the air and end up scaring the penguins. After they go away, the firefight restarts like nothing had happened.
An early chapter of Hellsing features Seras sleeping in a coffin after it was transported to Brazil. Before Alucard tries to wake her up, she breaks into a bizarre dream about her gun having the spirit of Baron Harkonnen that talks to her. As the scene keeps going, the art eventually devolves into random scribbles that only sort of look like humanoid shapes before Alucard eventually gets her up. The OVA has an equivalent sequence involving Alucard and a lot of spirits, most notably a Bruce Willis spirit.
Let it be noted that Seras' gun is named Harkonnen and Alucard's is Jackal.
In the Jack and the Beanstalk anime near the middle after bringing home some of the treasure and celebrating with his mom Jack's dog Crosby suddenly gains the ability to speak and he sings about how he loves the moon, after the song is over Crosby never speaks again and Jack points out how weird that was.
In Junjo Romantica, Miyagi, straight up until that point, suddenly grabbing a heartbroken Hiroki and attempting to kiss him. He never showed any serious interest in him before, and it's never mentioned again afterwards.
Near the end of the sixth episode of Kure Nai, all the characters (who are currently practicing for a play) suddenly burst into a seemingly-improvised song—out of nowhere—that has nothing to do with the play. (For one thing, all the names in the song are English, while the play is Japanese). The song goes on for a surprising amount of time before it stops, confuses everyone watching on, and just sort of... ends there.
Legend of Galactic Heroes, of all things, manages to get one in early in its second season, in the form of a bizarre sequence where Reinhard and Kircheis turn into angels and fly away into the sunset. It lasts all of five seconds, comes out of nowhere right during the middle of another character's speech, and has absolutely no bearing on the plot at hand (Reinhard and Kircheis both remain firmly on and in the latter's case, in the ground afterwards).
Worth noting that this is not actually something that happened. It was the illustration of a metaphor about their relationship, which is what Annerose was talking about. The "wings" metaphor recurs now and then throughout the series, though never again accompanied by the weird-as-hell imagery.
In the third season, we cut to a scene of Dusty in a fancy pirate outfit complete with a pirate hat with a large feather and a hook hand. We never see this outfit again. Ever. And no one mentions it.
The sing-along sequence in the Love Hina special "Kimi Sakura, Chiru Nakare!"
In fact, one can watch it like this: episodes 1-22, 30, 31, and 35-39.
Mahou Sensei Negima! has the infamous chapter 235 cheerfully starting with "Yes, we're worried about the captive Asuna, but right now..." Cue thirteen pages of "relaxation, healing, and group nakedness!" in the bath, including massive Skinship Groping of the cast by a girl who calls herself "Chichigami" (Breast Goddess), and their mild retaliation. This is never mentioned again.
Even more surreal because it includes the minor Reveal that the Sick and WrongPowered ArmorBounty Hunter from chapter 218 who is obsessed with "boobies" to the point of assaulting women so they can't resist... is actually the above said girl. Naturally, this reveal has no plot relevance whatsoever.
Naruto: Anime filler in general does a lot of weird stuff, but the weirdest, most out-of-nowhere moment might be when a villain was revealed to be a floating, talking, body-snatching wig, with zero explanation for how that came to be. She's killed almost immediately after this reveal, and is never mentioned again.
In one of the early episodes of NEEDLESS, a cat/worm creature comes out of Eve's ear as she is sleeping. Said cat/worm thing never appears again for the rest of the series, and its purpose is never explained either.
This disco zombie dance number in One Piece. There is no lead up beyond zombies shuffling to a mansion carrying a disco ball, and no mention of it ever made again, though the dance hall is mentioned as a possible location for a wedding reception later in a one-off gag.
The entire arc is a play on Michael Jackson's songs and videos — the name Thriller Bark (Thriller), Brook the skeleton's 45-degree angle pose joke (Smooth Criminal), and the aforementioned dancing zombies (disco dancing, but sadly not the music). But yes, it's a throwaway joke.
Speaking of which, try to forget for a moment that Michael Jackson's Thriller is a music video, and then think about the scene where he starts dancing with the zombies.
Generally though, Eiichiro Oda's very good at subverting this trope. Many events that might appear to be a Big Lipped Alligator Moment at first in fact turn out to be a Chekhov's Gun for much later.
Oda also subverts this trope by making all these seemingly random moments so ridiculously absurd that the audience just goes along with it.
During the Alabasta arc, there was the arrival of the Tsumegeri Guards, 4 Red Shirts that suddenly show up with no prior buildup whatsoever. They drink the Hero Water, which gives those who drink it tremendous strength, but results in instant death after 5 minutes. They try to attack Crocodile, who changes into sand, flies to the roof of a building, and mocks them while waiting for their deaths. Needless to say, they die shortly afterwards and despite how upset Vivi, Cobra, and Chaka were about this, it's never mentioned again. This scene did nothing to further the arc's plot.
Episode five of Ookami Kakushi starts out focusing on Hiroshi slowly realizing there's something not quite right about the town he moved to...and then suddenly cuts to a scene wherein a man is reunited with his two dogs in the antarctic, and gets eaten by said dogs. And then it turns out this is a commercial for an upcoming movie to be shown in Jougamachi. Of course, the only people who are actually shown seeing said commercial are Hiroshi's sister and father, who promptly go back to reading and never mention it again.
The end of Panty & Stocking with Garterbelt, where Stocking decides out of nowhere to actually kill Panty, and reveals that she has been a demon all along. It has been described as "Gainax trolling the fanbase" by fans.
In the Pokémon anime, Ash gets turned into a Pikachu by a magic spell that was supposed to make him capable of understanding Pokémon language (which, oddly, it doesn't; he still talks normally in that state). The transformation lasts the last 3 minutes of the episode and the first 3 seconds of the next — at which point it wears off. Totally irrelevant to the show's plot, and after it wears off, it's never mentioned again.
The episode "Island of the Giant Pokémon" features a scene where, after having endured an encounter with a giant mechanical Rhydon, Ash's Pokémon and Team Rocket's Pokémon are suddenly crying and drinking away their troubles at a oden stand that's attended by a Slowbro. The next morning they wake up in a completely different area and the Slowbro oden stand never explained or referenced again. In the Japanese version of that episode, there are captions translating the Pokémon's speech. Basically, the point of the scene is that the Pokémon are acting like stereotypical salarymen, going out late drinking with their coworkers and commiserating about their jobs. It's never explained or referenced again in that version either.
Also, near the end of the episode "The Case Of The K-9 Caper!", Jigglypuff just walks right in the middle of a semi-climactic scene and sings for 4 seconds (which surprisingly brings no one to sleep), then just walks off. Save for an off comment made by Ash immediately after (and a meaningless hook at the end of the episode), this has nothing to do with the episode at all, making it more of an extreme case of both this and Spotlight-Stealing Squad.
In Pikachu's Rescue Adventure, there's one strange scene, even by the standards of the setting, where Pikachu and company are treated to a ballet performed by Grass types and Water types.
The Nightmare segment in Puella Magi Madoka Magica The Movie: Rebellion is bizarre even by the standards of a movie about a psychological breakdown. It serves some narrative purpose in showing what Puella Magi do normally in Homura's Lotus-Eater Machine, but around the point where they defeat the big cuddly Nightmare monster by singing a nonsensical lullaby and turning it into a giant cake, things have pretty clearly entered this territory. As you might assume, Nightmares never show up again after that sequence, and the next few scenes are far less cute.
The manga Qwan derailed itself at the climax of its plot to transport the hero to a strange place full of people obsessed with their own hair and beards. This also happened close to the end of the third volume and the next volume still isn't out yet, almost pushing this into Gainax Ending territory.
In a movie that's already one hell of a Mind Screw, the brief moment in the Revolutionary Girl Utena movie when the strange, offbeat and surreal video of Nanami the cow is put in by the shadow girls manages to be one of these, coming right after a dramatic and horrifying scene, and of course never being mentioned again. Of course, according to Kunihiko Ikuhara, this was intentional. He's just that sort of guy. While the scene is so weird that even the shadowgirls are speechless, the video is kind of foreshadowing. If you think of Chuchu as Utena, The crocodile thing as Shiori and Nanami the cow as Akio... It makes sense if you think of the entire movie being on acid, but when even the characters are going "What the hell?!" in Utena you know it's something special.
"You're not the only one who can turn into a car!" After Utena turns into a car... The car-wash is never mentioned again (as well as Utena's clothes or transformation ability)
Robotech: The Macross Saga, in episode four, sees Rick and Minmay trapped deep within the title dimensional fortress for several days. Looking out of one of the ship's windows, they spy a giant tuna fish floating through space. Having almost run out of food, they immediately decide that it would be a good idea to go out into space and bring it inside the ship. Lacking spacesuits, Rick improvises by wrapping a towel around his helmet and holding his breath for the duration of the expedition. He succeeds in bringing the fish into the airlock, but in their haste they manage to slam the door down on the tuna, leaving only its head. Nonetheless, they still manage to make a meal out of it, which consists of little more than the fish head facing skyward in a simmering pan. Although their bizarre food acquisition plan can be explained by hunger-induced madness, the existence of the giant fish and its ability to withstand the effects of being teleported into the vacuum of space is never discussed, nor is the incident brought up again.
The fish came along with the rest of the surrounding ocean and Macross Island. It wasn't implied to be alive, merely intact — along with a lot of other debris. Vacuum isn't nearly so damaging as fiction tends to place it. Sure, it'll kill you, but you'll be an open-casket funeral.
Smile Pretty Cure! has the Akanbe eyecatch. The first episode which featured it had it because the episode was about April Fools Day (but in most parts of Japan, episode 10 had it), the second time, in episode 17 was really confusing as to why it was there, which really made it this trope. It however did not appear in the episode where Candy was kidnapped, and instead a Candy eyecatch was shown. Also, another way to tell if it's going to be on an episode (if you're watching it live) is if the last ad of the ad break is for Tanoshii Youchien when the plot is already about something scary. The exception to this is episode 39, when it was for the Sun-Star products Uki Uki Nurie and Himitsu no Jewelry Box, and on [[episode 47]], where it was for Seipan backpacks, which have nothing to do with the show in the first place.
And again in episode 28 due to it being an episode about a haunted school.
And yet again in episode 33, because it was about a yokai movie.
And in episode 39, due to the villains trying to give the Cinderella story a Bad Ending.
The absolute final time it could be seen was on episode 47. It's easy to explain why it was there.
In Seikimatsu Occult Gakuin Maya and Fumiaki discover nothing less than the Tree Of Life itself. This would be a tremendous find in its own right, but it is merely treated as a minor plot device and never mentioned again during the rest of the series.
Sonic X has an episode about Eggman becoming a wrestler. Not only does this have little impact on the story; it serves as a very bizarre contrast to the show's serious, story-based nature.
In another episode, Tails leans off a boat to save one of Eggman's robots, and stretches his arms and legs to absurd lengths to do so. This strange ability has never reappeared throughout the rest of the franchise.
Excalibur in Soul Eater is the living embodiment of this trope.
During the second season of Strike Witches, the girls find a treasure chest in the ocean and Lucchini attempts to use lock picks to open. The picks came from seemingly nowhere, disappear afterwards, and her lock-picking skill is never mentioned.
During the first episode of Black Butler's second season, we are introduced to Claude Faustus. During one scene, Claude starts randomly tap dancing before doing some sort of fancy ninja setting the table thing. The dancing never comes up again, and the reason for it is never explained.
The very first scene in Transformers Victory - in a Wild West town populated by Transformers and various other aliens, a pair of Decepticons arrive and are driven off by Star Saber, who seems to be a gunslinger, in front of a Christian church. This has nothing to do with the plot, and is never mentioned in any context throughout the show.
Due to Yoshihiro Togashi's near-zero understanding of how the English language works, every translation of Hunter × Hunter into English accidentally turn a backstory of a side character into this. The manga goes from the main characters in a fight to a story about a man who was abused by his father as a kid, became a drug kingpin, founded a nation, and was later eaten by ants, and then right back to the fight as if nothing happened.
The early chapters of Yu-Gi-Oh! are rather episodic in nature as it is, but are at least consistent. However, chapter 21, "Digital Pet Duel," is bizarrely out of place. It's the only story in the entire series where Dark Yugi doesn't show up and no shadow games are played and no magic is at work, and yet it is implied that the virtual pets are somehow alive and sentient in a universe established to be just like our own unless ancient magic is involved. These sentient LCD games and the whole incident is never brought up or acknowledged ever again.