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.
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 find a giant robot with a car for its head weird at all.
They do find it awesome, but more as a Cool Car, to the point that Megas is just one of many top competitors at a car show.
Or the fact 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.
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)
I Got A Rockets 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
An episode of South Park has a statue of the virgin Mary bleeding (out of her butt). The Pope then comes and says that the statue is actually menstruating, and that there is nothing particularly strange about that.
What the Pope actually said was along the lines of "a woman bleeding out of her vagina is in no way a miracle; women bleed out of their vaginas all the time".
And then there's Raisins, the kid version of Hooters. No adult bothered to question the idea of it.
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, no one seems to find 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 its head was a Hawaiian sheep and in another episode, 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 has a Running Gag where Ned's parents enter his room just as he's talking to his 6-foot-tall Shapeshifting pet newt Newton, upon which Newton quickly transforms into something supposedly innocuous... like the Venus de 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.
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 town librarian and a disgruntled stage magician is treated with boredom.
In the Family Guy episode "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 a few seconds to look at Peter before going back to reading.
In 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.
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.