In almost every Transformers series ever made, those who know about the eponymous Robots in Disguise seem to think giant space robots are an everyday occurrence.
The pilot episode of the original series has a plausible explanation for this. The Autobots were recognized by the nations of Earth for what they did to stop the Decepticons. So while most people will never have seen them before then (except for rare television appearances), most will likely say "Oh, so that's what they look like" and go about their business.
Likewise in Transformers Animated, the Autobots are recognized as Detroit's local superheroes, and so they are generally accepted as normal...and this is played with in the second season, where the destruction the battle with Megatron caused results in people being much more leery of them.
Given that Detroit already had supervillains (Angry Archer, Stilletto, Professor Princess) and superheroes (the Wraith), the giant space robots may not be the strangest thing the city's dealt with.
Detroit was also the capital of robotics technology in that universe. When Optimus Prime and his crew first emerge, battling a giant roach mutated by nanotechnology, local law enforcement just assumes that they are local inventor's latest project.
Played with in Transformers Cybertron, where giant transforming robots are actually an urban legend like Bigfoot. One wonders how that happened.
It is explained later in the series that there was a tribe of Decepticons imprisoned beneath a glacier who were the basis of all Earth's myths. Also, the series followed on from two others where the Transformers' existence was kept hushed up, although big mechanical men from outer space were never going to stay completely secret, so naturally something leaked out.
The 2007 live-action movie lampshades this and plays it for laughs. Optimus is confident enough in the Autobots' Earth disguises to assume that no one will question the sudden appearance of a fleet of expensive vehicles in the Witwickys' lawn. The denseness of civilians is also highlighted in the sequel but in both movies people (rightfully) start screaming when stuff starts blowing up.
Another aspect of the Transformers franchise that people should probably think is odd is the peculiar vehicle forms some of them choose; for example, one of the Combaticons is perfectly able to hide in Earth orbit without anyone commenting on a green space shuttle the same size as a tank. This was lampshaded in an episode of Animated, when Sentinel Prime and Ultra Magnus come to Earth; Sentinel claims he's scanned some Earth forms so they'll blend in, and Prowl remarks "Yes, no one will notice that" when Sentinel becomes a giant snow-plow (oddly similar to the one from the "Mr. Plow" episode of The Simpsons) and Ultra Magnus becomes a giant rolling missile platform.
In Danny Phantom, it took well until the later half of Season One before the people of Amity Park actually started noticing the ghosts in the town. This is taken to an interesting extreme when Valerie Gray's dad and his job security at Axiom Labs actually did try to stop him from leaving the building——but they clearly did not recognize him as a ghost. This might be somewhat explained that in the show's universe, ghost-hunters Jack and Maddie Fenton are viewed as well—-crazy; so why would anyone in the town even support that ghosts actually exist? It's not until one of Danny's most dangerous enemies starts blowing up the town that Amity Park finally begins paying disturbed notice.
In the Van Beuren Studios cartoon "Circus Capers", when Milton Mouse flies thru the ringmasters roof, Milton's girlfriend is too involved in her affair with the ringmaster to even glance over at him!
Or just stupidity. Vasquez doesn't seem to have much faith in the intelligence of the general populace, and this is never more evident than in Invader Zim.
Same thing goes for Spot/Scott Leadready II in Teacher's Pet, who is a dog that is able to pass as human by just standing up and covering his ears with a hat. He was also a blue dog to begin with.
Given his owner is chalk white, it probably comes under cartoon racial spectrums. However, nobody notices that he has a protuding jaw.
In Megas XLR, nobody seems to see a giant robot with a car for its head as anything but an especially Cool Car, to the point that Megas is just one of many top competitors at a car show. They also don't care that their city gets destroyed constantly.
Kim Possible centers around this trope; the main characters travel around the world to thwart evil scientists, fight monkeys that know kung-fu, and generally fight crime with self-learned She-Fu. While Kim has occasional fanclubs and interviews, for the most part, Kim leads a relatively normal high school life - right down to boyfriend issues and being scorned by the Alpha Bitch - without even using a Secret Identity. The characters also do not seem to be impressed about Kim's rocket scientist dad and brain surgeon mom, nor the abundance of child geniuses running amock.
And Drakken and Shego never attract attention for looking unusual. You'd think a green-skinned woman in a catsuit and a blue-skinned man in a labcoat who both happen to be wanted felons would catch people's attention, but no. Maybe no-one wants to say something about them being differently coloured.
You'd think people would remember a green-skinned woman who used to be a REAL superhero with super powers!
In the original G.I. Joe cartoon, no one ever takes any notice of incredibly colorful military uniforms, often with tons of armament on them, wondering the streets when the Joes are in an urban environment.
In Justice League and Teen Titans, nobody ever seems to notice the heroes wearing costumes in their mundane lives. They're neither starstruck that Wonder Woman is browsing their mall nor find it strange that green-skinned Beast Boy is at the arcade.
Averted in the CN movie Teen Titans: Trouble in Tokyo where Raven leads a one-woman bashfest on Beast Boy's estranged appearance when he marks that he won't be able to pick up chicks because his shirt is dirty.
The Simpsons plays this for laughs with a story within the show. Bartly (Bart) is surprised at almost everything, including, on one occasion, a doorknob. When a stool has been brought to life and walks right by him wearing a bowler hat, neither he nor the detective (Lisa) make any comment.
In one episode, Homer obtains the Auto-Dialer. When Prof. Frink (it's creator) finds out who has it, he presses a button on a remote control. Meanwhile, at the Simpson's house, the Auto-Dialer mechanically sprouts wheels and trys to escape from Homer, who just goes, "Oh, no you don't!" and removes the wheels.
In "You Only Move Twice" Homer is telling boss Hank Scorpio that he has to resign.....While ignoring the MASSIVE GUNFIGHT occurring around him, complete with explosions, acid vats, a soldier getting his neck snapped by a half naked chick (Which Homer notices but does not comment on) and finally Scorpio pulling out a Flamethrower and going to town on the government forces.
Scorpio: Homer, I'm disappointed but I think you need to do what's best for your family. [...] But Homer? On your way out, if you wanna kill somebody it would help me a lot. (straps on a flamethrower)
In "The Cad And The Hat", Rodd and Todd perform miracles and Ned simply chastises them for it. The episode ends with Bart's guilt turning into a giant monster. Mr. Burns notices it and is pretty casual about it.
I Got A Rocket's about a boy who is accompanied by a talking rocket - with eyes and a mouth. Nobody ever seems to think there's anything strange about a talking rocket casually floating around on the street.
A great number of people in We're Back! A Dinosaur's Story, do not seem to be impressed or curious about the talking dinosaurs that dropped from the sky!!!
MTV's Brothers Grunt were remarkably good at blending in with regular society, despite being gray veiny freaks dressed only in shorts and wingtips.
In Curious George, nobody seems to find the sight of a monkey walking around the city by himself -much less being treated as a person- as out of the ordinary.
Chip 'n Dale Rescue Rangers. A lot of the cats, dogs, mice, chipmunks, birds, etc. wear clothes, but none of the humans seem to notice.
Arguably Justified as most people who do see them think they're escaped pets.
Semi-subverted in Martha Speaks: people who find out that a dog can talk are surprised, but get used it to it VERY quickly. And then don't think twice about getting advice from a dog
"Bloody Mary" has a statue of the virgin Mary bleeding (out of her butt). The Pope then comes and declares that it isn't a miracle becase "chicks bleed out of their vaginas all the time."
"Raisins" has Raisins, the kid version of Hooters. No adult bothered to question the idea of it.
"A Nightmare on Face Time" has two people doing this to each other:
Randy: What are you doing? Shelly:(setting a shelf on fire) Nothing, dad. Go back to killing the family. Randy: Okay.
"The Mysterion Trilogy": When men see Cthulhu, they're supposed to go insane. Cartman, however, is able to look Cthulhu straight in the eye with no reaction whatsoever.
The The Adventures of Super Mario Bros. 3 episode "Toddler Terrors of Time Travel" has Mario and Luigi get turned into babies, but still have their mustaches, right before they visit the woman whose bathtub they're supposed to unclog. When they arrive at her doorstep, she doesn't seem to notice that these babies have mustaches.
He did say that the woman was "a little daffy", and she failed to see anything weird about Bowser and Ludwig as "Koopa & Kid Costume Plumbers".
On Lilo & Stitch: The Series, and the whole Lilo & Stitch franchise in general, no one seems to find Stitch and all the experiments working around the island to be all that strange, or even remotely believe they're aliens.
Oh, it goes even further. Some of the townspeople who do manage to pull their heads out of their asses and notice them compare them to animals that in no way resemble the experiments (or any real-world animal for that matter). In two instances, a pair of tourists thought Yaarp, a blue, four-armed, ring-tailed experiment with a giant megaphone-like antenna on his head, was a Hawaiian sheep, and in another episode, they mistook Kixx, a bulky purple experiment with four oversized arms, for a wild pig.
However, it is subverted on some occasions. The crossover with American Dragon: Jake Long, for example, had the cast of that show coming to Hawaii to investigate reports of "magical creatures."
The town of Danville from Phineas and Ferb has a local Mad Scientist community, an organization of Cool Hat wearing secret agent animals and two young supergeniuses with short attention spans, so naturally, all sorts of bizarre things seem to happen, almost always crisscrossing with other bizarre things as well. When the boys' new pet lizard suddenly grows fifty feet or their latest invention turns to broccoli, however, no one bats an eye, except for Candace, an Only Sane Girl who seems to be going crazy as a result. (And Linda somehow never sees any of it...)
Ned's Newt: Nobody ever seems to mind that Newton is a six-foot-tall humanoid blue newt, even if he's walking around without a Paper-Thin Disguise. Despite this, sometimes Ned seems to be concerned that his parents or the other citizens will find out about Newton's existence. A Running Gag is for Ned's parents to enter his room just as he's talking to Newton, upon which Newton quickly transforms into something supposedly innocuous... like the Venus of Milo, or "the big metal thingy for affixing a ship." Ned's parents comment on this, but never seem to mind.
Nobody ever finds it strange that Scooby-Doo is a talking dog.
Slightly discussed in the episode, "The Weird Winds of Winona", in which Mystery Inc. meets the team behind Speed Buggy. While Fred, Daphne, Velma, and Shaggy seem unfazed by the idea of a talking car, Scooby does take notice.
Speed Buggy: Come on, Scooby. Climb in.
Scooby: No way!
Shaggy: Go on, Scoob. It's only a car.
Scooby: That talks?
Debbie: That's a strange question from a dog that talks.
Played with in the Disney animated shortSocial Lion, where a lion ends up in NYC, only to find out that nobody pays the slightest attention to the fact that he's a lion, not even when he roars. It's not until he tries wearing clothes that everyone suddenly realizes what he really is, and panics.
An episode of SpongeBob SquarePants has the Flying Dutchman temporarily move in with SpongeBob, and the Dutchman begins scaring him every chance he gets. Eventually SpongeBob becomes desensitized to the Dutchman's pranks and starts treating them like everyday occurrences, so he's unfazed by the Dutchman's horror show later on with him taking on increasingly bizarre forms.
In part 1 of the Garfield and Friends episode "Grape Expectations", Roy goes to the supermarket in order to buy one grape to replace the missing one in the stash, and there are actually humans there. Nobody batted an eyelash about the fact that there was a talking rooster in the store.
It says a lot about the strength of Pinkie Pie's Weirdness Coupon in My Little Pony: Friendship Is Magic that few ponies bat an eye at her doing things such as sneezing confetti or wearing a haystack. In fact in the latter case Rainbow Dash not only greets her casually, but freaks out for a completely unrelated reason.
Twilight Sparkle was initially freaked out by Pinkie's weirdness, but eventually she gives up trying to figure it out and just accepts it.
The setting can result in the viewers having difficulty in telling which sights are considered interesting and which aren't. The townsfolk react to a stampeding herd of bunnies with panic and terror, while a Wizard Duel between the two strongest magic talents alive (outside the princesses) is treated more like a spectator sport.
Post season 3, you'd think Twilight becoming an alicorn would draw some notice nearing that of the Princesses, but that doesn't seem to be the case. For example, in "Rarity Takes Manehattan", when she attempts to call for a carriage, nopony even gives her the time of day.
In "Testing, Testing, 1, 2, 3" the entire town puts on a history performance about the Wonderbolts for Rainbow Dash as she flies overhead; she was so depressed at the time, she didn't notice it was actually happening until it was over.
In "The Cutie Re-Mark", Twilight and Spike go on a time traveling adventure. The child version of Rainbow Dash is the only character who seems to notice or care that Twilight is an alicorn.
Family Guy - A show set in a world where actual talking dogs and babies are normal:
In "Fast Times at Buddy Cianci Jr. High", Peter attempts to convert the house staircase into a water slide and injures himself going down it. Brian, who by now is used to Peter's antics, simply ignores his agonized groans telling him "I'm not going to call the hospital because you won't learn anything if I do."
A similar incident occurs in "Breaking Out is Hard to Do" when Peter attempts to do some sexual act that requires Lois' assistance without her (she was incarcerated at the time) and ends up falling down the stairs. Brian take his eyes off of his newspaper for all of one second to look at Peter before going back to reading.
In "Total Recall", after Stewie and Brian spend the episode trying to rescue Rupert from a toy factory after he's recalled, Rupert's eye comes off and Stewie swallows it and chokes to death. When Chris comes by, he yells to Lois completely unphased "Mom, Stewie's dead!"
On Gaspard and Lisa, the classmates don't seem to mind that there are two talking dogs with bandanas, walking on their hind legs. Nope.
Most of the historical figures and often all past civilians from Time Squad don't seem surprised that they've been visited by time travellers from the future.
Justified in the case of Buffalo Bill since he was a conspiracy theorist who had suspected that he was being watched by people from the future to begin with.
In Can You Teach My Alligator Manners?, EVERYBODY thinks that a giant, manner-learning, walking, talking alligator who is a kid's pet is just a normal sight.
In Teenage Mutant Ninja Turtles (2012) the turtles are generally pretty good about being stealthy when on the streets, but there is a lot of stuff going on in New York City that really should raise more notice. Probably most blatant when the Shellraiser, a subway car converted into a monster truck that's as wide as a two lane street, is driving around in plain view of several pedestrians, and no one so much as takes a second glance.
Uncle Grandpa is both everyone's uncle and everyone's grandfather... somehow. He's also a Reality Warper with various supernatural abilities including being in multiple places at the same time, and is over 1 billion years old (by virtue of being the oldest person in the RV). Nobody ever finds any of this odd.
One episode of Mission Hill has Gus walking down the street with, get ready for this, a knife embedded into his head to which a birdcage (containing a bird that happened to fly in) is welded to, that also has two faucets, a menorah, a mobile, a fake flower, a tennis racket, and an umbrella all attached to it. While he's surrounded by people all marvelling over it, he passes some Rabbis one of which comments "That man is insane. Hanukkah is next week!"
Most residents of Beach City from Steven Universe seem oddly unfazed by the presence of three magical aliens, a magic half-alien kid, and the various weirdness said things entail around town. Humanity is vaguely aware of the fact that there are supernatural beings in the world, but choose to ignore it because it's easier.
Eventually revealed that the Crystal Gems lived in the Beach City area before the humans arrived, making them as interesting as the waves or the sand. Out of towners are a bit more surprised by the magic women, but the gems and their artifacts have been on Earth for at least the whole of human history, and have had various visible effects on the world, some subtle, some not.
None of the human characters in We Bare Bears seem to be bothered by the main characters being bears.
In Rick and Morty, the neighborhood usually seems perfectly casual around aliens, otherworldly technology and other oddities. This may be a case of Mundane Fantastic, as when the episode calls for it, the humans will react accordingly.
In most episodes of The Grim Adventures of Billy & Mandy, almost none of the mortal characters seem to be bothered by the sight of The Grim Reaper. There's even a point near the beginning of the first movie where a paperboy drives by and tells him "Morning, Death!"
Gary the Rat is a six-foot-tall anthropomorphic rat. In fact, he's the only Funny Animal on the entire planet. The people of New York are remarkably blasé about this, though.
In 2 Stupid Dogs, nobody seems to find it odd that the two titular dogs are capable of speech. The dogs are even treated as if they are human beings on occasion, as they were allowed to compete in a game show in the episode "Let's Make a Right Price" and Little Dog was allowed to enlist in the army in the episode "Post Office".
In "I Want Baked Beans" on Little Princess, Puss (the palace cat) comes up two failed plans to swipe sausages from the table - first trying to hook one wish a fishing line and then dressing up in a ninja outfit complete with Mission: Impossible style music and having Scruff (the palace dog) operate a device to lower him down to the bowl on the table. In both cases, the King, Queen and Little Princess, all of which are sitting at the table, either don't notice or aren't bothered by the unusual activity going on.
At Flying Rhino Junior High, no one bats at eye at the fact that both the principle and janitor are an anthropromorphic rhino and pig, respectively, which is lampshaded in the theme song: "The principal's a rhino and no one's asking why". People also take to The Phantom's reality warping attacks on the school rather well, though they might have just gotten used to them. Principal Mulligan, meanwhile, is stated to suffer from a Weirdness Censor.
In Star vs. the Forces of Evil, the title character Star Butterfly is an alien princess with a magic wand, whose spells tend to be both brightly-colored and highly destructive. Particularly in the season 1, it's commonplace for a gang of monsters to attack her on the streets. She has also done things like permanently transforming her homeroom teacher into a troll. None of this is treated as even remotely unusual by the residents of Echo Creek.
Dexter's Laboratory: It's common for Dexter's parents and ordinary bystanders to ignore any outright weird occurrences; for example, at the end of the episode "Maternal Combat" Dad comes back home, doesn't seem to notice that the house is a smoking ruin, and casually says hello to the two highly advanced androids standing in the hallway. In "Double Trouble" Dad likewise doesn't seem to care about the countless clones of his daughter and her friends running around the house.
Kung Fu Dino Posse: The people of Megalopolis don't bat an eye at the sight of talking anthropomorphic dinosaurs walking around town.