A rare scary example occurs in Marble Hornets with Alex in Entry #46. The Operator appears behind him in his own house, but unlike Jay who bolts as soon as it happens, Alex stays put and is later found to be okay. Of course, this is foreshadowing to Alex's betrayal.
In the That Guy with the Glasses anniversary special Kickassia, the citizens of Molossia (all five of them) treat an invasion and then a rebellion as this, simply going "Mmmm-hmmm!" and reading their magazines. The only time any of them showed any reaction was when they were freed, and it was still just a look up from the magazine and a confused "What?"
After much pleading from others, Spoony finally gives into his inner madness and transforms into Dr. Insano. The Nostalgia Critic's reaction? "Oh hey! You gave into the madness, that's awesome," and turns back to his TV.
Also from TGWTG, in The Nostalgia Critic's review of My Pet Monster, he criticizes the characters for acting nonchalant about how the protagonist keeps turning into a monster. The Critic then walks off, and comes across The Other Guy reading The Far Side... and is a velociraptor. Both the Critic and The Other Guy act calmly about it. "I'm a dinosaur", indeed.
Deconstructed in The Review Must Go On, as Karl completely ruins Donnie's hopes of everything being okay by having the same dinosaur head. The music freaks and the very normal Donnie looks he's going to break down crying.
Linkara sometimes complains about this trope in his comic reviews, where characters will act like someone flying or having super strength is nothing. He often says "Be impressed, dammit!" when this happens.
Sometimes, you've got to love the page pictures that go with some Wikipedia articles. Apparently, this is run-of-the-mill for Lego minifigures.
An inversion in Indiada Jodes:
Kid: I have a paper that leads to a thing. Indy: DID YOU SAY A THING?
Chad Vader: He works in an ordinary, present-day Earth supermarket, but dresses like Darth Vader, uses The Force, and wields a lightsaber. No-one finds this unusual.
In the Game Grumps spin-off Table Flip, nobody seems perturbed by 'Him', the mysterious cloaked figure who shows up whenever the rules need clarifying. Danny seems to be the only person who questions it, and is freaked out by everyone else's indifference.
Sal in It's Walky has incredibly long, straight hair. It's the first thing anyone would notice about her. So does she cut it or even attempt to hide it while on the lam? Of course not! It gets lampshaded in one comic.
In Bee and Puppycat, Bee has a tendency to under-react to events that would freak out lots of people, such as being (briefly) sentenced to incineration.
In Part 1 after her inexplicably found dog(or maybe a cat) gets a letter transported through it's bell collar all she can manage is groaning. She does lampshade that there better not be anything cryptic in it.
Basically everybody's reaction to everything in Welcome to Night Vale, with the exception of the visiting scientists, and even they're getting used to it. Ominous coloured helicopters watching your children? Check the colour chart to make sure they aren't really dangerous. A giant, sentient glow cloud raining dead-animals on the town? Let's make it the president of the PTA. An eighteen foot tall, five-headed dragon? He runs a blog, got arrested for fraud and is running for mayor. Confronted with a terrible existential dread about the meaningless of your life? Drink to forget.
This is how a lot of people react in Poohs Adventures. Talking stuffed animals? Act like nothing. Living, breathing trains? Act like nothing.
Life or death battle in iBlade headquarters between the son of the outgoing CEO and his best friend revealed to be a 'Deathless' infiltrator. Worth a glance, but back to whatever you're doing.