‘I wonder what else lives down here that we don't know about?’ said Carrot. ‘Well, there's always the invisible squid-like creature that sucks all the air out of—’ Rincewind began, but sarcasm did not carry very well out here. The universe diluted it. The huge, black, solemn eyes in the sky withered it.
More recently, Asakura was rendered completely speechless upon seeing several people get wiped from existence.
In the first season finale of Code Geass, when Nina completes her super-bomb, Lloyd does this. The fact that the "Pudding Earl" got deadly serious is enough to convince Rakshata that he's not bluffing when he says how dangerous it is.
Deadpan SnarkerKyon is momentarily reduced to incoherent choking sounds in the Haruhi Suzumiyamovie when Ryoko Asakura shows up in class acting like she'd never tried to kill him. Considering he can ordinarily keep up, verbally at least, with Nagato, Koizumi and Tsuruya, it's a memorable moment.
In The DCU, it's often considered that the ultimate way to show just how bad things have gotten is to have The Joker stop laughing.
Or that something is exceptionally satisfying (possibly disturbingly so) when Batman smiles.
The best example being when Harley Quinn, who spends every waking moment with (and fawning over) the Joker, Ax-Crazy king of maniacal laughter, reacts to Batman's laughter with a meekly frightened:
Harley: ...I've never seen you laugh before... I don't think I like it! Cut it out, you're giving me the creeps!
When the Justice League nearly got taken out by Batman's contingency plans in the Tower of Babel arc, someone shouted an order at Plastic Man and he replied with "On it." The response was "...What, no jokes?" "This is not funny."
Lenny in Shade, the Changing Man was always good for a snark, no matter how dire the situation. Her Sarcasm Failure was a result of an author, an unwitting personality plunderer, who had written her into his book, and shocked her enough to drive her to a suicide attempt.
Speedball (a looong time before his Penance days) starts makes a sneeze joke about somebody called 'Ashu' (or similar), but when he starts explaining, he gives up with "even I can't make jokes right now".
In Doom Patrol, Cliff Steele is often snarky about the situations he finds himself in. Upon seeing Orqith, a parallel dimension of bone and decay: "All of a sudden, I can't think of anything remotely funny to say".
Calvin & Hobbes: The Series has the former character trying to snark at a rather heartfelt speech about parental relationships, and not doing a very good job at it.
Kup, the grizzled veteran in 1986's Transformers: The Movie, often told war stories comparing situations to battles he'd been in. Eventually they discover Unicrondevouring their home planet.
In Manhattan, Woody Allen gets dumped when his girlfriend reveals that she's going back to his (married, though soon to be divorced) best friend. You can see him clearly reaching for a standard Woody one-liner, but instead he can only stammer, "I'm... I'm stunned, I'm, I'm, I'm...."
Harry from The Journey Of Natty Gann does this in a very subtle way. He spends most of the film making sarcastic remarks to Natty. He tells her that he last went to the west coast with his "old man" and she responds with "Your dad?" He looks like he's about to make some retort like "No, my sister." Instead he lets his guard down and tells her about his dad's death.
You know the situation is either particularly dire or somehow personal when Marco stops making sarcastic jokes in Animorphs.
Jake actually has to take him aside at one point and order him to start cracking jokes, because his seriousness is frightening the others.
Similarly, you know things are bad when Richie Tozier stops cracking jokes in IT. (Though sometimes averted - as a Motor Mouth with poor impulse control, he slips up from time to time, notably mouthing off to Henry Bowerstwice in a row, straight to his face when the big lummox falls over.)
"Pathetic, With the whole wide world of ear-related humor before you, you go for holey?"
On the other hand, when Fred dies, we can safely assume George doesn't start cracking jokes about it.
Likewise, Mad Eye's death made the twins shut up.
In American Gods, Mr. Nancy (Anansi) starts out as a Cool Old Guy who is perpetually joking. When things start going bad for the old gods, the protagonist notes that Nancy complete stops smiling and telling jokes. Only when things are settled does he return to his former carefree attitude.
In the true-crime book Homicide: A Year On The Killing Streets (upon which Homicide Life On The Street was based), one of the recurring observations is that homicide cops can be very, very snarky on crime scenes, as they have to deal with a great deal of unpleasantness in their day-to-day working lives and use wit as something of a defense mechanism. This, then, serves to make the discovery of the body of eight-year-old Latonya Kim Wallace and the investigation into the scene of the crime particularly powerful; it's simply noted that there's no jokes, no sarcastic comments, just a lot of grim and serious-faced cops doing their jobs.
This was later shown to be a good reaction: when he does start cracking jokes, it annoys her. And because it annoys her, she freezes the water in his eyes. He's reduced to whimpering in pain and crying Tears of Blood for a while.
Harry generally goes light on the sarcasm around Nicodemus as well, for much the same reasons. Nicodemus is too much of a No Nonsense Nemesis to get affected by it anyway.
A strange example of mostly dramatic but with a hint of bitter comedic aftertaste in GONE. PLAGUE has Diana at a loss of word when her boyfriend declares himself king and tells her to Get the fuck off his island, thus breaking up with her. In the next book, After having a torture birth aged 15 in a hot, pitch dark mine she has this reaction when, just minutes after birth, she is expected by Drake to just "Get up and walk."
Live Action TV
House: When the title character starts wearing a serious expression and talking respectfully to the patients and their relatives, it's an extremely ominous sign.
Unless he's doing it consciously to mess with the other's heads, of course.
Or just...weird. In the opening of the infamous "Fur & Loathing in Las Vegas", Grissom and Catherine come across a dead man in a furry costume; both of them perceived it to be a dead animal from afar. When seeing what it actually is, both are weirded out. Catherine looks to Grissom for the requisite one-liner, perceiving Grissom to not be weirded out by anything, but Grissom continues to look weirded out silently into the opening credits.
Horatio in CSI: Miami does this also. One such example: when his old friend is blown up and instead of his usual quip he just stares at the smoldering house in horror.
MASH: This show attempted this with Hawkeye, but overdid the seriousness.
The Futurama parody, where Hawkeye is a robot (named 'iHawk') who switches between IRREVERENT and MAUDLIN modes, is an indication of the result.
iHawk (maudlin): This isn't a war, it's a murder.
iHawk (irreverent):(as Groucho Marx) Dis isn't a war, it's a moider!
Subverted in Buffy the Vampire Slayer: Anya's irreverence comes out of genuine cluelessness, not an attempt to be funny. So when Buffy's mother dies, Anya behaves as normal, and infuriates the other characters. However, her explanation of why she isn't acting like any normal human with normal sensitivities would act (she's not a normal human, and she doesn't "understand... how this all happens... how we go through this...") is one of the most heartfelt of her character arc, and does basically follow this trope.
At least until it's revealed that Anya, when she was still a normal human and hadn't become a vengeance demon yet, acted just as cluelessly.
Yet even Anya-as-a-human probably didn't have the attitude of "It's mortal and stupid!" towards death.
Xander is a better fit to the original trope.
One example of Xander playing this one for comedy (there are probably many others): in the Season 4 episode "Something Blue," Willow accidentally, and unbeknownst to the rest of the gang, casts a spell that makes Spike and Buffy fall in love and become engaged.
Buffy: Spike and I are getting married!
Xander: How- What- How?
Giles: Three excellent questions.
As is Giles, who can usually be counted on for a dry remark. In the seventh season, as the cast falls once again into mocking Xander's dating habits, Giles rather sharply points out that they are fighting a war for their very survival.
From Dexter: The usually lecherous Masuka becomes stone serious when investigating the crime scene where a cop was attacked.
Deb: What, no jokes about providing gross sexual comfort in a time of crisis?
Masuka: My friend was stabbed, and he might die.
It's actually used as a barometer of Masuka's mental wellbeing at times. Later that episode:
Masuka: Hey Morgan, wanna sit on my lap when we're done and tell me what you want for Christmas?
Deb: And he's back!
Similarly, we get an impression of how gruesome a murder scene is when Dexter himself (a blood-spatter analyst who is also a serial killer who chops up his victims) gets nauseous at the sight of it. It's also a hint that the scene had been constructed specifically to remind him of his repressed memories regarding his mother's brutal murder.
In Season 3, Masuka gets one of his articles published. He's very happy and proud about this and gives autographed copies of the journal to his co-workers who, we later learn, never bothered to read the article. Masuka's personality undergoes an abrupt change after this. When the officers ask him why, he tells them "You hurt my feelings."
A good deal of the characters from Scrubs (in fact, the entire show seems to follow this trope).
Blackadder does this at the end of the fourth season. The main character, who is probably sarcasm made flesh, remains serious when Darling, Baldrick and George admit to being scared before they all charge into a battle in World War I. The episode itself became this trope in its surprisingly-reverent conclusion,
An inversion of this can be seen with Simon Cowell. If he stops being mean or sarcastic even with his body language, you know the person he's watching is good. From Britain's Got Talent alone: Paul Potts, Connie Talbot, Susan Boyle, and Julian Smith.
For example, take Hollie Steel. Simon's not thrilled with her because she looks like a typical wannabe-ballerina, and has his hand over the buzzer. The camera cuts to her beginning to sing, and the next shot is him absolutely shocked.
Susan Boyle. From rolling his eyes, to shock, to fawning.
In all fairness though, it's been indicated as fairly likely that these reaction shots aren't always the ones from those contestants, since, you know, it's a TV show and everything (Skip to about 05:20 for the relevant chunk)
As Boy Meets World went on Eric got sillier, more erratic and just plain damn weird, but when he did get serious you knew things were bad. Like the time a prank war caused a serious fault in the friendship and he was the only one willing to work it out, the silliest thing he did was pick up Rachel and drag her back into the classroom Mr. Feeny had locked them in and sit on her so she could read what he had written.
"Lose one friend, lose all friends, lose yourself."
The Middleman subverts this in "The Vampiric Puppet Lamentation":
Psych played this straight, then subverted it, when Shawn is targeted by a Serial Killer. Shawn quickly loses his snark as he was overwhelmed by the pressure. As the situation grows more dire, Shawn convinces Gus that he should joke around for both of them. Which Gus does, resulting in hilariously awkward and terrible prop comedy.
Technically, it was subverted, then played straight. Shawn never lost his ability to crack jokes while crime-solving (in fact, he outright states that if he isn't able to joke, the bad guy wins) and that is why Gus starts behaving ridiculously. The trope is then played deadly straight later in the episode when the bad guy kidnaps Shawn's mom.
Shawn also plays this trope out during the episode Gus Walks into a Bank, when Gus was in serious danger and Shawn couldn't be there with him.
Early on in Firefly when Malcolm discovers River stored in a crate, his initial response is a dull "Huh". He recovers more or less instantly and begins snarking at Simon, however.
Certain news stories on The Daily Show can get this reaction out of Jon Stewart.
Whenever Morgan and Garcia of Criminal Minds aren't bantering and flirting, you know things are bad.
Reid: (On the phone, sick with anthrax and getting worse.) What, no goofy Garcia nickname for me this time?
Garcia: No. I can't be my cheery self when you are where you are.
Music example: Dead Kennedys' 12" single In God We Trust Inc. The Single includes rants against the religious right, Ronald Reagan (We Got Bigger Problems Now, sung to the tune of California Uber Alles from their first album) and against neo-nazis that flocked their gigs after misunderstanding some of their songs (Nazi Punks Fuck Off, arguably the Sarcasm Failure of the band).
Tom Lehrer's response to Henry Kissinger receiving the 1973 Nobel Peace Prize:
Political satire is obsolete.
Throughout Disgaea, Etna has delivered descriptions of the next chapter that are nothing like what happens. The one time she did, nobody believed her. Then for the final chapter, when things have hit the fan, her description is perfectly accurate. Everyone panics. She is less than amused.
Legacy of Kain has a particularly amazing example. Throughout the entire, multiple-game-long series, main character Kain has always spoken faux-Shakespeare dialogue, and he always mocks his opponents; he's the equivalent of the game universe's Dracula, and he's so powerful that in a normal series he'd be a Game Breaker. However, when he sees the Elder God, a horrific Lovecraftian monster responsible for everything he's suffered in the series, his only response is a genuinely bewildered, "What in the hell?" It's a sign of how utterly overwhelming the truth is that even Kain can't come up with a good taunt.
And just before that, you get to see one of the few times Kain genuinely smiles, because Moebius is there, and has no idea that Kain is about to kill him. Again. As one Fauxtivational Poster put it, "Kain is smiling. Run for your lives."
Beckett from Vampire: The Masquerade - Bloodlines is a vampire who spends most of his encounter with the player being sarcastic. But he suffers this in the endgame, after he (presumably) learns the truth about the Ankharan Sarcophagus. He flees town immediately afterwards.
Garret from Thief is usually a prime Deadpan Snarker and has wry, or at least interested, insights into a lot of things you see during your missions and cutscenes. He usually shuts up during the more frightening areas of the game. The Shalebridge Cradle from the third is especially notable: Garret speaks exactly two lines during the entire mission, and both of them are more to the effect of Oh Crap.
One of the routes you can take in Dragon Age II is to turn Hawke into a snarker who turns every situation into a joke, no matter how appropriate that may be. One mission in the second act involves someone stealing qunari gunpowder, except it's not gunpowder, it's a poison gas that makes all non-qunari go insane and kill everything. The elf responsible tries to make bombs to blow up a street to frame the qunari, but instead winds up poisoning lots of people, and doesn't entirely see it as a setback. Upon learning this, Silly!Hawke's response is:
"You were going to kill lots of people anyways? That's... not funny at all, really."
There's also the quest in which Leandra is taken by a serial killer and Hawke has to follow a trail of her blood to find her. Every version of Hawke, be they The Paragon or a Deadpan Snarker or a Blood Knight, will sound horrified and panicky.
Iji has the Scrambler, a Silliness Switch that either turns the game into a "Blind Idiot" Translation or makes the lines even crazier ("You promised me a pony... with missiles... I want a missile pony!"). However, near the end of the game, Asha tries to kill your Voice with an Internet Connection, Iji's brother Dan. When Iji finally kills Asha, she screams, "That's what you get, you bastard! That's what you get for trying to kill him!" Even with the Scrambler on, this line is almost untouched.
Final Fantasy X: there are a few moments when the normally stoicDeadpan Snarker Lulu gets this. Most notably when it is revealed that Sin will come back eternally, no matter what the Teachings say and how much people repent. Also, when Tidus pulls the final reveal on the party right before the final boss, if she's got the highest affection score with him, her reaction is an utterly bewildered "What are you talking about?!".
"Dang, man, couldn't you have summoned Beetlejuice? At least he's funny."
In the later areas of the Sea, when discussing the hideous eldritch powers that have corrupted Mom and Dad Sea Monkey, the game is completely devoid of jokes.
An example in Sly 3: Honor Among Thieves, when Bentley is explaining to Sly how they'll have to cheat in the ACES dogfighting competition since they have only one plane compared to the 15 each on the two opposing teams.
Sly: Normally I'd make some sarcastic remark about how "overcome I am by your confidence in me", but those are some pretty grim odds.
Looking for Group: Richard can usually be trusted to have a snarky comment or off-beat action in most situations. But after seeing a vision of his past self and asked if it was really him, all he can come up with a simple "Pass".
Danny Phantom: Happens twice in one episode. At first, it was Skulker, completely ignoring Danny and not saying a word. Later in the episode, it's Danny, who is searching for his sister. He attacks Skulker and demands answers, no quips involved.
Skulker: That's odd, no witty banter? Danny: Not in the mood!
In The Spectacular Spider Man, when the Green Goblin's glider slams into a building while flying backwards, just before impact the Goblin jumps off the glider, does a backflip in midair, and lands on the glider on the other side of the building.
In Avatar The Last Airbender, near the end of the series, Sokka and Toph are dangling off an airship. Sokka's space sword and boomerang are gone, and things look really bad for them. This may be the only point in the whole series that Toph and Sokka, the two snarkiest characters in the series, are both acting serious.
He also does this when he accidentally spills to Rachel that Ross is in love with her. He sputters "crystal duck" a couple of times and then descends into meaningless babble.
And in a Throw It In example: at one point Chandler mocks Joey's attire by saying "Donald Trump called and he wants his blue blazer black" (instead of "back"). Matthew Perry genuinely messed up the line, but the other actors took advantage of it and went with it, pointing out the mistake and making fun of snarky Chandler. (Monica: "No, no, you messed it up! You're stupid.")
In one episode of Dads Army, the platoon are covered in mud after saving Pike from a bog and are marching back into town when they spot Hodges (the local greengrocer/ARP Chief Warden and Captain Mainwaring's rival), Mainwaring mentions that he's probably got some "smart-alek remark" and tells the platoon to march smartly and just ignore him. Hodges is practically quivering with anticipation at being given such a prime opportunity to try and take the wind out of Mainwaring's sails, only for him not to think of anything to say as the platoon marches past un-snarked. The verger (who was with Hodges at the time) remarked that he looked like he was about to have a heart attack.
A gag-oriented version occurred on Penn & Teller: Bullshit! during the episode on fast food. When the issue of the "Soda Tax" was raised they cut to a scene of Teller fiddling with a wide array of props. Penn went on to explain that the two of them found the concept of taxing the sales of soft drinks made with government-subsidized ingredients so asinine they couldn't come up with a magic trick to adequately express it.
Certain news stories on The Daily Show can get this reaction out of Jon Stewart. His reaction to Newt Gingrich using a "describe yourself in one word" question to describe himself as "cheerful" (after using an entire debate prophesying doom, gloom and general unpleasantness if he's not elected)? Walk off the stage.
The Rachel Maddow Show: Rachel Maddow was reduced to this in an attempt to respond to a somewhat poorly worded Republican speech, as seen here.
Rachel Maddow: I know that I am paid to talk for a living. I am incapable of doing what I'm paid to do right now.
A Dilbert comic ended with Dogbert telling Dilbert that "I'd mock you, but the challenge is gone."
Stand Up Comedy
Occurs during Jeff Dunham's routine with his puppets Peanut & Jose Jalapeno on a Stick. Peanut and Jose begin conversing in Spanish, and Jeff asks them to stop because it leaves him left out. The usually smart-assed Peanut is reduced to a "HUH?!", and when Jeff's explanation is that he can't speak Spanish, Peanut stops his sarcastic comment before it can even begin to just stare at him.
Lewis Black had a variation in a bit about the excesses of the rich:
"They bought houses; second and third homes that they decorated and didn't live in—but they got a tax write-off for''—and I'd have a joke about that, but it makes me too FUCKING ANGRY!!!"
The World Ends with You. After Beat betrays the Reapers for Neku in the first day of the third week, Kariya and Uzuki warn him that 'he's treading on thin ice'. The character responds triumphantly that it couldn't possibly happen; Shibuya is too hot for there to be any ice for him to tread on. Despite both Neku and Kariya being prime Deadpan Snarkers, Sarcasm Failure immediately strikes everyone present.
Also in Vampire: The Masquerade - Bloodlines, Beckett suffers a humorous form if you end up having a discussion on Kindred origins with him as a Malkavian. While the 'normal' player characters have theories he's already well-acquainted with, the Malkavian ones are a bit more... Unique.
Beckett: ...Can't say I've heard that one before...
Throughout God Hand, Gene has a mocking quip for pretty much every scenario... except the first time he meets the Mad Midget Five. After a stunned second, the best he can do is to choke out, "Douchebags!"
Homestar Runner: Strong Bad suffers from second degree Sarcasm Failure several times; the most common causes would be the title character and Coach Z.
"...Ow. Just... ow" is still his only response upon recovery.
Not uncommon responses in Real Life... at least, among the empathetic crowd.
Erfworld: In this◊ strip, they are in a deadly serious situation...but what finally makes Jackstop joking is Parson's absurd suggestion that they might actually win.
The Nostalgia Critic: This happens to the Critic a bit, at which point the Running Gag of him literally aborting the joke occurs. Thinking about this (perhaps a little too much) leads to wondering how often these are unintentional and put in during editing, vs. how many of these are pre-scripted. Fantastically done in the Bio-Dome review
Joey Lauren Adams: (affectionately) "There is something about a man who can lick his own back..."
Nostalgia Critic: (beat, stunned) "What am I supposed to say to that?"
Mark, of Mark Reads Twilight and Mark Reads Harry Potter fame is often completely lost for words when he reads something particularly painful or an amazing plot twist is revealed. At said points, he will usually resort to either gifs or keyboard smashing.
Film Brain's review of Mega Piranha eventually turned out a scene where the only response was "... I got nothing."
After Linkara reads in X-Men #424 that Nightcrawler is a priest with lustful desires, he states that he isn't going to touch that one.
In The Ant and the Aardvark cartoon "Technology Phooey," the Aardvark's quicksand trap backfires on him, prompting him to quip "I'd say something right now, but it would only be censored!"
The Batman: The Animated Series episode "Almost Got 'Im" involves several members of Batman's Rogues Gallery telling each other stories of their most brilliant attempts to kill Batman that almost succeeded. The Joker, who is saving his story for last, spends most of the episode quipping at and mocking the other villains' attempts. However, Killer Croc's 'brilliant plan' is so dumb Joker can only stare dumbfounded at him, with this sort of "what-the-hell-is-this-guy-even-doing-here" expression frozen on his face. For those of you who are curious, Killer Croc's "brilliant attempt" at trying to kill Batman was throwing a rock at him.