Sailor Moon was, most of the time, a Magical Girl show set in the modern day, where the only non-ordinary elements are the Sailor Team itself and the season-specific villain faction. The beach episodes (once a season), however, were strange exceptions: episode 20 had Usagi, Ami and Rei confronted by an (apparently) real ghost, not connected to the Dark Kingdom in any way it is actually the result of little esper girl manifesting something she couldn't control. Episode 67 featured no villains and thus no need for the girls to use their powers, instead presenting a couple of living dinosaurs. Seriously.
Episode 67 had so little to do with the overall plot, it was actually left out of DVD releases of the series. The DVD release simply skips over it.
A startling example occurs in the second season of the ghost-and-swordmanship filled Jubei-chan, where it's revealed that the reason the Human Popsicle villainess knows about 21th century customs is because upon thawing, she was raised by Talking Animals.
Mazinger Z is a sci-fi Mecha Show. Several times Kouji Kabuto has said (in the original manga) that he does not believe in ghosts or living corpses. Then in a Crossover movie with ''Devilman, he accidentally wakes up a demon and spends the remain of the movie finding and fighting demons and devils.
Patlabor featured two episodes that clashed with the show's otherwise stringent policy of depicting "real life, but with robots:" One with a prehistoric giant monster, and another with a haunted building full of ghosts.
There were a few other giant monsters, as well. Though all of them had sorta-scientific rationales behind them, they still stretched the Willing Suspension of Disbelief by playing fast & loose with the Square/Cube Law (more so than the relatively modest sized Humongous Mecha of the title, anyway). The first OAV featured a giant monster that was created by a Mad Scientist doing experiments on abiogenesis that somehow rapidly evolved from an amoeba to a humanoid Kaiju that inexplicably had Yamazaki's face. The TV series had a Patlabor sized giant rat created by growth hormone experiments & the monster from the 3rd movie, which was a grotesque giant zombie/fish thing created from genetically altered human cancer cells & alien DNA from a meteor.
The prehistoric monster story also played with the unreality by having hyper-rational But Not Too Foreign cop Kanuka Clancy insisting the creature must be some sort of dinosaur and practically using the trope quote as a Madness Mantra, while dreamy Genki Girl Noa insists on calling "him" a dragon. It's "him" according to Noa because "He had a deep voice".
In Infinite Ryvius, Straw Vulcan Stein Heigar is quite upset when the spaceship Grey Geshpenst suddenly goes One-Winged Angel, transforming from a conventional-appearing vessel to a massive organic sphere, insisting that it violates all logic. (He is unaware that the Grey Geshpenst is a Living Ship).
Parodied, like many other things, in Gintama; specifically, the episode where Gintoki and co. team up with the Shinsengumi to fight a supposed ghost:
Shinpachi: Could it be there's really a ghost?
Gintoki: Huh? I don't believe in things that can't be scientifically sustained like ghosts. Though I do believe in the Continent of Mu. (beat) This is ridiculous. I don't feel like goofing around with you guys. Let's go back.
Shinpachi: What is this? (Gintoki is holding hands with him and Kagura)
Gintoki: What do you mean? I was just worried that you two might be afraid or something.
Kagura: Gin-chan's hand's all sweaty, this is disgusting.
Gintoki: Huh? What are you talking about?
Okita: Ah. The woman in the red kimono [the ghost in question; in this case, Okita's just trolling them, as customary].
(Gintoki leaps into a cupboard and assumes fetal position)
Shinpachi: What are you doing, Gin-san?
Gintoki: Uh, nothing. I just saw a gate to the Continent of Mu.
Ghost in the Shell: Man-Machine Interface arbitrarily features a psychic who keeps astrally manifesting to the protagonist as a raccoon dog and a teenaged girl whose body is made out of a dragon, commenting on her activities in a Trickster-like manner. Motoko's own comment on her first manifestation is "How unscientific" (added with a footnote that it's unscientific to dismiss a phenomenon on the drop of the hat, implying that the author has his own opinions on the subject).
L, the master detective in Death Note, has solved the world's toughest mysteries, but he is completely stumped as to Kira's modus operandi because he doesn't believe in the supernatural — at most, he allows that Kira must have psychic killing abilities or mental powers, but not a something out of (pseudo) Japanese mythology. When he's finally presented with evidence that shinigami are real, he has a screaming freak-out followed by a short breakdown. Light does his best to convince him there's no such thing as shinigami, while Ryuuk grins in the background.
Many of the Gundam series (read: everything but ∀ Gundam and G Gundam) go out of their way to portray everything as realistically as possible, down to giving a justification for apparent Square/Cube Law violations. They also features psychics and ghosts.
That really,reallyweirdCloverfield prequel manga. As an example, it's revealed the main character was created by a cult using human and monster DNA, and that the cult intended to use him to control the monster, which responds to an emotion-powered orb in the character's body.
Played for Laughs in Great Teacher Onizuka, which is a (slightly exaggerated) slice of life series about the trials and tribulations of a high school teacher: Onizuka is momentarily possessed by ghosts after he takes on the very stressful job of picking up the remains of those who committed suicide by jumping in front of trains. Miyabi and Fujiyoshi also meet the ghost of a child killed in a road accident, though they don't realize it after seeing a sign talking about his death.
The most recent Astérix book, Asterix and The Falling Sky, features two groups of aliens fighting for control of the magic potion. With Superman clones. And lasers. In an otherwise Low Fantasy version of Ancient Rome.
Depending on the Writer, Batman goes from "deep distrust of magic, but respects those who do use it" to "dismissing the supernatural as 'stuff we'll figure out eventually, but it ain't magic'".
Reed Richards also believes that magic is simply another kind of science, and one he has no interest in studying. This, despite being closely allied with magic-users like Doctor Strange and Agatha Harkness. In "Unthinkable," Strange tries but fails to teach Reed magic and, in desperation, gives him a magical gauntlet that runs on humility, forcing Reed to spend an entire fight loudly proclaiming that he has no idea what he's doing.
Some of the humor in Atomic Robo comes from Lampshade Hanging on things that are too ridiculous for its universe, such as giant ants. This really comes into play, however, when Robo fights the talking raptor Dr. Dinosaur, who claims to have time-traveled from the death of the dinosaurs with a crystal-powered time machine. Robo points out the grossly bad science in this backstory before pointing out that Dr. Dinosaur is probably just a genetic experiment gone wrong (which is implied to be true).
In the Tintin story Flight 714, we had a thrilling hijack plot and Tintin & Co. being trapped on a remote island. And then out of the blue... Aliens!
In one Ramba story, Ramba (an assassin who normally takes on gangsters, drug dealers, terrorists, etc.) encounters cultists who are summoning a demon. She steals their magic book and uses a spell from it to transform her cat into a monster that battles the demon. This is the only appearance of the supernatural in the entire series.
The death scene for the main villain; Bond wrestles him into a pool of sharks but, before either of them get eviscerated by them, he pulls out a compressed gas pellet and sticks it into the villain's mouth. This has the cartoonish effect of causing him to literally inflate like a blimp and float up towards the ceiling, getting bigger until he eventually bursts. Making things even more cartoonish is that he pops exactly like a balloon, with no blood and just rubbery shreds left over. It was around this time in the movie series where things started to get more campy and ludicrous.
The apparently functional Voodoo prescience and a Dragon who actually comes back from the dead like the deity he's named for/impersonating/possibly is.
The case in Indiana Jones and the Kingdom of the Crystal Skull. On one hand, this was the film which introduced interdimensional alien beings into a series which had firmly rested on the magical side of Magic Versus Science. On the other hand, this is perhaps justified in that the three earlier movies were set in the '30s and were based on 1930s serials, which focused on magic and fantasy and had Nazis as the bad guys. The fourth movie was set twenty years later, and based on serials from the '50s, which featured more sci-fi and Communists as the antagonists.
The Prestige starts off telling the story of two rival stage magicians. Every trick is an explained illusion. Then Nikola Tesla shows up with self-lighting lightbulbs, airborne electrical currents, and a duplication machine.
Played for laughs in Disney's Bolt when aliens are introduced into the new episode of the show. Rhino is shown looking particularly unimpressed by the changes.
Blade has this to anyone one not familiar with the original comic book. Vampires are explained in Doing in the Wizard fashion (vampirism is a literal virus, they are burned by UV light, they react to garlic but not to crosses, etc) then in the film climax the Big Bad uses a mystic ritual to become the avatar of the vampire's blood god to issue the vampire apocalypse. Despite this he is still killed in a mundane manner.
Many fans of Jeff Lindsay's Dexter books were disappointed with the third installment, wherein the Dark Passenger which joins the titular serial killer in his "fun" is pretty much proved to be some sort of primordial creature that comes to certain humans during times of great emotional pain instead of just being part of a (completely understandable) dissociative disorder.
Leslie Charteris' The Saint often encountered the paranormal, though he mostly had mundane adventures facing black mailers, gangsters, kidnappers, and so forth. He encountered advanced technology sought by Dr. Rayt Marius (a no plans, no back-up situation) in The Last Hero, oversized ants in The Man Who Liked Ants, machine to produce gold, advanced aeronautics, zombies, and the Loch Ness Monster. The anthology The Fantastic Saint collects most of these stories.
Some paperback original heroes of the 1970's such as The Penetrator switched back and forth from mundane gangster foes to enemies with technology that outpaced the 20th century.
James Lee Burke's Robicheaux series featured the paranormal in the book and film In the Electric Mist (With the Confederate Dead).
The 87th Precinct novel Ghosts involves the paranormal, and in The Encyclopedia of Science Fiction notes this serves as a detriment to the novel as a detection.
The Decameron suffers from this in one tale, where the mundane medieval setting is disturbed by an actual vision of Hell.
In the book The Great Detectives, Walter Gibson wrote an article of reminiscence on his work on The Shadow, and he noted that some stories approached or crossed into science fiction, while other Shadow stories stood as conventional crime thrillers.
The Skylark Series by EE Doc Smith may get extremely far-fetched with the science, but it was always science, or at least plausibly something like science. Then came the series finale, in which the collective witches of the universe got together with the main heroes to turn their collective magical willpower to overcoming the villains' telepaths and transporting a whole solar system into another galaxy, which is then set on fire to burn for a thousand years. May have some of the details off there, but it was not a little disconcerting, what with the effective Mood Whiplash.
The Pure Dead series has this kind of moments. Its mostly about fantasy, but the second book introduces cloning. Given how it was handled (basically the clones were incubated in a duck corpse and ended up as being small sized, red versions of the humans that they were cloned from) it hardly matters.
Dennis Wheatley's adventurer the Duc de Richlieau debuted in a non-paranormal adventure novel. However, Wheatley featured de Richlieau in the novel The Devil Rides Out (1934) where he encounters the modern wizard Damien Mocata, who has actual paranormal powers. The Duc de Richlieau would alternate between paranormal adventures such as Strange Conflict and Gateway to Hell and mundane adventures such as The Golden Spaniard, Codeword-Golden Fleece, The Second Seal, The Prisoner in the Mask, Vendetta in Spain and Dangerous Inheritance.
Enoch Root in Cryptonomicon appears to not age in the half century between his appearances in both the World War II era and the modern era. In The Baroque Cycle, this is elaborated upon, but to someone just reading Cryptonomicon the presence of this unaging man sees pretty much no explanation.
The final Doc Savage novel Up From Earth's Center has Doc clashing with someone who might have a demon and visiting somewhere that might have been Hell.
A Hallowe'en special of Boy Meets World has Eric, in typical Eric fashion, convinced that Jack's new girlfriend is a witch. As it turns out, she is a witch, and the episode builds to the attempted ritual sacrifice of Jack and Shawn. Then Eric hooks up with Sabrina, who turns Shawn into a toad. (Another episode featured Sabrina, as part of a crossover, but all she did was set off Something Completely Different — in the 1940's — with no other supernatural elements.)
During the last few episodes of Felicity, a to-that-point relatively tame romantic drama about college life, the main character began to wonder whether or not she'd chosen the right man in her life. So her friend cast a spell that sent her back in time a few years. No, really.
Gradually took over the show in Family Matters, with the many and varied inventions of Steve Urkel. It started as a middle-class Sitcom starring predominantly black characters. However, after Urkel's ascent to popularity and building of gadgets, rather than this feeling out-of-place it was effectively retooled to become the Wacky Adventures Of Steve Urkel, Harmless But Mad Scientist.
In the Veronica Mars episode "Normal Is the Watchword" our titular heroine is saved by a hallucination of (or possibly the actual spirit of) her dead best friend Lilly. Lilly had appeared frequently the previous season (as Veronica tried to solve her murder), but it had certainly been implied she was not a literal ghost, just Veronica's way of working through her emotions and thoughts. At least until "Normal Is the Watchword", when Lilly's sudden and unexplained appearance distracted her friend from getting on a doomed bus.
Which is in keeping with the supernatural events he eventually runs into as an adult.
And the original framing sequence (which was removed from the DVD release) implied that it was a ghost story that old Indy was telling to some kids on Halloween.
Buffy has fought robots several times, including one becoming a major part of the sixth season, despite the show being virtually entirely focused on magic and demons and the like. Angel has as well, though less frequently and in a less important role.
It actually makes the spinoff cartoon with the alien girl a little less nonsensical.
Japanese Spider-Man, episode 37 of 41. A man who specializes in the occult warns that King Enma from Hell is coming. He comes. Note that for the last 36 episodes, the series has entirely been based on sci-fi.
JAG usually kept itself grounded in something resembling reality... except for the episodes involving Mac's psychic powers and Bud's near-death experience. And then there was that one time a villainous plan involving a fake ghostly vision was foiled by the appearance of a real ghost.
The fourth season finale of NCIS (a show that is usually firmly grounded in reality) had a doctor encounter a little girl who was heavily implied to be the Angel Of Death.
An episode of The Guiding Light actually featured a character gaining superpowers after a freak accident with Halloween decorations.
Invoked on LOST every time the current plot elements shift from pseudo-scientific discussions and theories to mythological and religious elements. Which happened quite often.
In one episode of The Unit, Kim Brown is investigated because she knew vague details of a mission which she claimed to have learned in a dream. The Colonel brings in a psychic specialist, and by the end of the episode (even though none of the characters realize it), the audience is pretty convinced that Kim is a high-level psychic medium.
Married... with Children had aliens as a plot element in one episode, and also the whole trip to England plot arc which was based on a 17th century curse by a witch. By this point though the show had basically become a live action cartoon that ran on Negative Continuity and thus these episodes were largely brushed off by fans.
The gap between the two shows is perfectly illustrated in the episode "13.1" by an exchange between Claudia and Fargo (paraphrased):
(Claudia has a ring on her finger, causing her hand to glow brightly) Fargo: Is it somehow increasing your own bioluminescence? Claudia:(shrugs) It used to belong to Ben Franklin!
The New Adventures Of Robin Hood was mostly a Xena homage Fantasy, but the episode "Marion Saves the Day" was about an alien crash-landing in Sherwood and repairing his space-ship in time before the Sheriff dissected him.
Bones has Booth, at one point, trapped in a room with a bomb, and a door that he's not strong enough to open on his own. He's also hallucinating a soldier buddy that he knows is dead, and that he calls a hallucination several times to further reinforce the point. Long story short, he convinces the hallucination to help him open the door, thereby escaping death by explosion. And if you're thinking that he summoned up some Heroic Willpower, at the end of the episode, the Squints, a team composed entirely of genius-level academics, points out that the door really was impossible for one man to open. Eventually, the hallucination is explained by Booth's brain tumor, but the mystery of the door is left unsolved.
Doctor Who slowly crossed the line from at least trying to sound scientific at all times to allowing the supernatural (though usually calling it something else). The dividing line is probably The Key To Time stories in the Tom Baker Years, which introduced the White and Black Guardians.
Perhaps best exemplified in The Impossible Planet, where the Doctor encounters a being that claims to be the Devil (not a devil, but THEDevil). The Doctor refuses to believe it, theorizing that it's just some Sufficiently Advanced Alien trying to sound impressive. The episode leaves the whole matter ambiguous.
Benson was generally a perfectly straightforward sitcom, but it had a couple of episodes like this, like the time the mansion staff acquires a robot, and the Halloween episode where Benson ends up challenging Death to a game of Trivial Pursuit to save the lives of a busload of children. Plus there was the dream sequence episode where Benson and Krauss are the only two humans left on Earth.
This is somewhat more justified than most examples on this page due to Benson being a spin-off of Soap, which featured similarly outlandish elements. Jessica Tate even appeared in a later episode of Benson as a ghost (though she said she was actually in a coma).
Special Unit 2 was a short-lived UPN drama that worked from the idea that all the monsters of myth were just evolutionary off-shoots from existing species. Then came the episode where a "Link" so powerful he could be assumed to be the Devil sought an artifact that could grant him power if he performed a magical ritual. For a show that had been all "science we don't understand," it took a pretty damn hard turn into "magic."
Merlin deals with fantasy tropes, but one (widely disliked) episode has him battle a manticore that introduces the rather sci-fi concept of parallel dimensions.
Of course, plenty of mythologies around the world, including the British ones Merlin is a derivitive of, include the concept of 'other worlds' so sci-fi hardly has the monopoly on this. It's merely the way 'other worlds' are introduced that would slot the concept into a sci-fi or fantasy.
Naturally Sadie was teen drama/sitcom about a girl coping with the vagarcies of high school life. Except for the episode "Ghouls Just want To Have Fun" which featured Hal's girlfriend Tabitha handing out wristbands that turned people into zombies.
Diagnosis: Murder was a light-hearted murder mystery programme which involved a lot of Contrived Coincidences but nothing actually unbelievable. Except that one episode where the murderer was an honest-to-gods vampire. Who died when she telikenetically flew herself into a chair leg. And was never spoken of again.
How I Met Your Mother parodies this. The entire show is ridiculous, but it focuses almost entirely on the (physically-possible if really unlikely) exploits of a group of mundane, if wacky, modern-day New Yorkers. But every so often they throw in a one-shot gag about time travel, just because.
In the second season of Twin Peaks, Major Briggs's experience with Project Blue Book is often alluded to. The context strongly suggests that if the show hadn't been cancelled, it would have veered towards science-fiction.
The early 1980s detective series Matt Houston had one episode where a faked alien abduction was somehow involved in a crime the eponymous hero was investigating. Then, at about the 3/4 mark of the show, Houston, driving by himself, is actually abducted by the stereotypical little gray buggers. He doesn't remember it happening, there's no witnesses, and it has no effect whatsoever on the plot of the episode, and is never mentioned again.
Seven Days mostly deals with Time Travel. Said Time Travel equipment came from a crashed alien ship; so there's sci-fi. Then there's the episode where the main character stops a nuclear war started by Satan.
Several scholars of Greek Tragedy have claimed this to be the case for the Oedipus story. The confines of realistic human tragedy seem to always be at odds with the riddle-spewing, man-eating, she-beast in the backstory.
The Odyssey is not technically a supernatural story. Aside from the unfalsifiable secret movements of various gods, all of the monster-fighting and sorcery takes place within Odysseus's narration; the main text is only telling you what the man said happened to him. Only the battle with the suitors at the end definitely happens, and that part of the story is merely unlikely, not impossible.
Later, in Super Robot Wars Original Generation, a new robot pilot shows up with two magical talking cats in tow.
In fact, this happened so often in Super Robot Wars Original Generation that a bridge operator teases his vice-captain that when he leaves the ship, he'll miss the vice-captain's constant moments of this. The Vice-Captain doesn't know what he's talking about, but almost instantly has another one of these moments...
This was a common complaint about Metal Gear Solid 2, although it was probably deliberate in order to play with the making-the-player-doubt-the-canon theme. Vamp is a super-strong pseudo-vampire who can predict where bullets are about to hit him and come back from the dead after being shot. Ocelot claims "There is no such thing as miracles or the super-natural, only cutting-edge technology." Minutes later, his ghost-possessed arm hijacks his body.Except it doesn't.
The original line was just something about technology being able to manufacture miracles. The translator decided to jazz it up a little and wasn't real into paying attention.
Which makes a lot more sense, considering that in the first Metal Gear Solid, he was teamed up with a guy who could float around and throw things with his mind.
Ōkami starts out as a Far East version of Fractured Fairy Tale, including references to people from the Celestial Plain in the heavens. Sounds appropriately mystical at first, but you eventually see these people's vessels and the game portrays them as spaceships (one - described the locals as a "metal bamboo shoot" - even looks like a traditional rocket). The Big Bad itself is practically a robot.
The first Rayman game is a light-hearted platformer where you fight musical instruments and colorful wildlife. The second has you fighting evil robot pirates who have blown up the heart of the world and enslaved all of your friends.
Given the ludicrousness of the series in general, that probably falls under Mood Whiplash more than this trope.
The "silly clowns" option in Quest For Glory II, a game that takes place in a middle-eastern fantasy setting. Granted, these games basically run on Anachronism Stew combined with an overabundance of cheesy gags, but there's just something about seeing a brightly dressed clown walk through the streets of the Sultan's palace.
The Ace Attorney games are in a realistic-ish setting, with spirit channeling appearing on the side, holding no real effect on the game for the most part, and not appearing in the latter games, which while featuring rather unlikely concepts, feature nothing on the scale of mediums.
In the Touhou side manga Wild and Horned Hermit, Kanako uses this trope when doing the cold fusion experiment after Reimu wonders if there would be demons or spirits emerging instead of just bubbling water. The whole use is rather ironic considering they are conducting a scientific experiment in Gensokyo, the land where everything fantastic exists.
The final Nevada level in Tomb Raider III' is pretty consistent in theme, ranging from a high security area in the middle of a desert and transitioning to a secret government lab experimenting on aliens and have an alien spaceship locked away in a room. However, at one point, you see a pair of orcas/whales in a tank. The whales are just there without any explanation at all and they severely clash with the theme of the level. The only reason you would jump into their tank is to collect the level's last secret.
This reaction, taken to extremelyFan Dumb levels (death threats were involved), forced a significant change to Heroes of Might and Magic III: Armageddon's Blade: originally the expansion pack was supposed to be centered around a science fiction faction, the Forge, and the attempts to stop it from taking over the world, but that had to be thrown out and another story quickly come up with. Whether this trope is an accurate reaction is... more complex: the setting was a clear Science Fantasy one, so looked at from that perspective the Forge was in keeping with genre conventions. Heroes, on the other hand, had previously only loosely alluded to the science fiction elements in ways that didn't make clear they were science fiction elements, so looked at from the perspective of the series it was a breach of genre conventions.
Transformers Generation One was primarily a sci-fi show centered around giant robots. However, there were several occasions where the plot delved into supernatural areas—in one episode they ran into a wizard in the past, in another they dealt with a Quintesson who used magic, and two episodes were devoted to Starscream's ghost.
The Simpsons was an ordinary show at first, but became a Fantasy Kitchen Sink starting with Season 10. For example, there's the episode "Goo Goo Gai Pan" (Season 16) which features, amongst other gems, Homer's heart being ripped out of his chest,then put back in with no after-effects whatsoever. Also, there are dragons. Or something.
Scooby-Doo has occasionally been known to replace the guy in a monster mask with an actual monster.
Generally, if Shaggy and Scooby are alone (or with Scrappy), the monsters are real. If Fred or Velma is there, they aren't. The films, both live-action and Direct-to-Video, usually have real monsters regardless of their cast.
The Daria episode "Depth Takes a Holiday" involves Daria meeting personifications of the holidays asking her to find other missing personifications of them who have run off. Quite different for a show mostly about life in high school. Do yourself a favor and don't bring it up to fans.
The Mysterious Cities of Gold is set around the conquistador times, and is about men in search for El Dorado, and cities full of Gold. While their are some semi-mythical elements (such as Esteban being the "Child of the Sun" and that the Incas have fairly sophisticated fantasy-esque technology), it was always kept in the theme of the period and explained in terms of what was available at the time. Then out of nowhere, the aliens are revealed and watching the protagonists on television screens...
The Flintstones: The Great Gazoo is a space alien in a modern stone age setting.
In Batman Beyond, Bruce Wayne's response to Terry McGinnis telling him of a suspected haunting is "why not?", but that the incident in question is rather... childish. He's right, of course.
Bruce: These people believe anything they can't explain is magic. Terry: Naturally, you don't believe in those kind of things. Bruce: Of course I do. I've Seen It All. Demons, witch boys, immortals, zombies. But this thing, I don't know, it just feels so... so high school.