No Big Deal

Remarkable and bizarre occurrences seem commonplace, yet everyday citizens take no notice and go on with their lives as if nothing out of the ordinary ever happens.

See also Invisible to Normals, Weirdness Censor, Plot Technology, Unusually Uninteresting Sight. Not to be confused with Somebody Else's Problem.

Anime and Manga

 * In Bleach half the populace of Ichigo's home town have (as a direct consequence of his and presence) become aware of the spirit world and able to see it. But that doesn't mean anyone acts strangely when they see samurai fighting monsters in the park; most write it off as filming for a movie.
 * The fact that Shinigami are Invisible to Normals helps a bit in this regard.
 * Actually Asano, upon picking up the ability to see spirits, is rightfully terrified of all the monsters and scary samurai he's now seeing.
 * Pretty much every single odd situation or event in FLCL is at most a minor deal to the inhabitants of Mabase. Giant factory that spouts smoke once every day? Must be good for the economy. TV-faced robot reading porn magazines at the convenience store? Gets a few odd looks. The cat ears sprouting from Naota's head get exposed to the rest of his classmates, magically transfer over to Ninamori, who then starts sprouting a giant robot from her head right in the classroom? Just another day in Mabase. Naota saves the city by  Well, that's worth offering Naota a bit of casual praise, but don't go overboard with it...

Comic Books

 * The inhabitants of superhero cities like Metropolis or Marvel New York tend to get pretty jaded about the constant supervillain attacks and what-not.

Film

 * In Men in Black II, a giant alien worm with an MIB agent on its back goes barreling at high speed down a subway tunnel and through a station. The commuters look up, watch it pass - and go back to what they were doing. Hey, it's New York.
 * In Blade, Blade beats up a vampire familiar dressed as a police officer in the middle of a crowded street. None of the passer bys seem to notice.
 * Either that or they don't want to attract the attention of someone brazen (or crazy) enough to beat up a cop in broad daylight. Or some of both.
 * In Hop, during his time in Hollywood, E.B. is noticed by Hugh Hefner, a group of soul singers, a waitress, and David Hasselhoff. None of them are freaked out by the presence of a talking rabbit, even though Fred was extremely freaked out by it. Only the Hoff offers so much as a Hand Wave as to why.

Literature

 * In The Dresden Files, Harry Dresden often remarks on people's capacity to ignore or rationally explain away supernatural events in their midst, however strange or flashy, like his riding a re-animated dinosaur skeleton through the streets of Chicago. (In the Harry Potter universe, the Ministry of Magic spends a lot of effort and casts a lot of memory spells to keep the existence of the magical world secret from muggles; in the Dresdenverse, the White Council of wizards has better things to do.)
 * The Left Behind series of apocalyptic Christian fiction is a gigantic offender of this, in the bad way. Before the apocalypse even starts, Israel is sneak-attacked by the entire Russian nuclear arsenal and its air force, but all the missiles are harmless and the attack fleet dies without even a single Israeli casualty. Yet nobody seems to pay this blatant divine intervention that should probably spark a worldwide conversion to Judaism very much attention. People react with a similar blase attitude to the Rapture, rather than a mass realization that "holy crap the premillennial dispensationalist Christians were right, let's all convert to fundamentalist Christianity." The movie version even has Antichrist Nicolai use the Rapture as an excuse for atheism somehow, as it proves that there is no God and "just us." This can be partially explained, perhaps, as being due to copious amounts of demonic mind control on non-Christians. However, this approach still doesn't work as many converted Christians still don't really connect the dots as should be obvious.
 * If a missile attack on Indonesia failed for utterly inexplicable reasons, would the majority of the world suddenly become Muslim?
 * Maybe, maybe not - there isn't anywhere near the religious significance attached to Indonesia as there is to Israel. But why would anybody throw far more nukes than necessary at any target, without any apparent provocation? You do not attempt to defend the Left Behind series.

Live Action TV

 * In Buffy the Vampire Slayer, denizens of Sunnydale just shrugged off the vamp attacks as the work of angel-dusted gang members with barbecue forks. During Series Three, we learn that the mayor and the school principal have been participating in the cover-up for their own nefarious purposes, and feeding the "usual line" about gangs on PCP to the news outlets. A little Lampshade Hanging disguised as a plot point...?
 * Slightly subverted
 * Doctor Who hangs a lampshade on this during "Remembrance of the Daleks". When Ace objects that a Dalek spaceship can't have just landed in the middle of the day, in central London because surely people would remember it, the Doctor points out several other of his adventures which remain apparently unknown to ordinary folk. "Your species," he notes "has an amazing capacity for self-deception." This is further elaborated on in the revival series, when large-scale occurrences are often blamed by the government on hallucinogenic drugs slipped into the water supply by terrorists.
 * Averted in the new series' third season finale, where the Master references a number of the Doctor's former "disaster in England" episodes during a political speech as his politician alter-ego.
 * Also averted in the Christmas Special--London is deserted, since they've realized aliens keep attacking at Christmas. (Good thing they did, too, because when the Titanic did crash in the alternate 'Turn Left' universe the city got nuked).
 * In an episode of Star Trek: The Next Generation, Data is transported back to 1890's San Francisco. Nobody there seems to care about or indeed even notice his obvious differences from normal humans. Those who do just shrug it off when he says he's French. Of course the android can speak it like a native.
 * Mark Twain, for one, notices the difference, constantly referring to Data as an "albino". Other than his skin and eye colorations, there really aren't any obvious external differences between Data and natural humanoids.

Video Games
"...Lowlifes. ...Shameless filthy wretches. How you celebrate my ascension with such joy. Hailing the very one whom you have condemned for generations. Have you no shame? What happened to the evil, ruthless sorceress from your fantasies? The cold-blooded tyrant that slaughtered countless men and destroyed many nations? Where is she now? She stands before your very eyes to become your new ruler. HAHAHAHAHA."
 * In Fable 2, at the end of the game you can get a one-shot-use-it-now-irreversible gender-changing potion. On this troper's second playthrough, I used it on my married, male character, then went home. My character's wife and children Did. Not. Bat. An Eye. The children stopped addressing him as Dad and started calling him Mum. At least protected sex wasn't necessary any more...
 * Edea's speech in Final Fantasy VIII:

Web Comics

 * Almost the entire citizenry of Generictown in The Inexplicable Adventures of Bob.
 * The world of Sluggy Freelance has got this so bad that, at one point, a woman has a conversation with a talking ferret, and only when mentioning it to a friend later does she realize that this is somehow unusual.
 * A large part of the plot of Megatokyo is this.

Western Animation

 * Sometimes seen in the citizens of Townsville in Powerpuff Girls. In fact, one of the promos for the show shown on the Cartoon Network consisted of a live-action version of a Townsville man calmly going to work, ignoring the various aliens, giant monsters, and supervillains he passes along the way, despite one of them briefly turning him into a dog.
 * Townsville's denizens do have limits though. In one episode the Girls are forced to use a "Dynamo" invented by Professor Utonium to defeat a particularly tough monster. They succeed but end up destroying the entire town in the process, prompting the Mayor to make the Girls promise to never use the Dynamo again and the entire town (including the Narrator) to be rather miffed at Professor Utonium.
 * People hang out with the Autobots in most Transformers shows like there was nothing at all odd about it. Nobody ever runs away from them, screaming and babbling about huge metal terrors from beyond the stars. The 2007 movie, however, makes this a plot point: Sam is absolutely terrified when he sees his car transform into a giant robot, and doesn't trust it until it saves him from Barricade.