Hellsing: Rip van Winkle does this in the 4th OVA when Alucard suddenly smashes her alarm clock, alerting her of his presence. She does it again when he catches the bullet she was firing at him in his mouth.
Jonah: A VeggieTales Movie. Jonah, Khalil, and the Pirates all take turns at dramatic gasping when they see just what "The Slap of No Return" is, before all doing a simultaneous gasp.
In one scene of Open Season 2, a slightly aged Elliot does a long gasp after a slightly older Boog says to a slightly older Giselle, "We're partners, right?".
In one scene of Open Season 3, Giselle, Gisela, and Giselita all gasp after Doug (who is disguised as Boog) yells at them to go get him more berries and to massage his paws.
In Shrek 2, the three girls who discover the newly human Shrek dramatically gasp (and smile) when Donkey says "First we need to get you out of those clothes."
There is a scene in Alvin and the Chipmunks: The Squeakquel where the Chipmunks and Chipettes gasp upon seeing each other.
Several women in the crowd during the climax of Mulan do this when the Huns show up, complete with shaking their heads 'no'.
Everyone (and we do mean everyone) in the town of Swallow Falls does this in Cloudy with a Chance of Meatballs after Flint's food machine produces a rain of cheeseburgers. Flint's gasp is especially and hilariously protracted.
Vegan Police: On April 4th at 7:30 pm, you partook of a plate of chicken parmesan. Envy: GASP! Todd:[nervously] Chicken isn't vegan?
Christopher Lloyd is really good at these; a perfect example comes in the first Back to the Future, where Doc Brown gets a classic reaction face when a burning wind-up car drives into a pile of oily rags.
During the first dinner at Dundrillin Castle in Aunt Dimity and the Deep Blue Sea, Sir Percy is recounting a local ghost story, and he's just relayed a creepy detail when the lights go out. Lori's reaction: "I gasped, nearly stabbed myself in the face with a forkful of lamb, and knocked over my water glass."
Live Action TV
Frasier. Frasier does this when enraptured with something, a lot.
Sonny With A Chance does this all the time, but usually they're parodying their fictional TV show "MacKenzie Falls".
Community: "[It's] the noise people make when they're offended in all the movies that Annie rents."
Done Narmingly in Discworld Noir. The film noir-ish protagonist Lewton is usually pretty hard-boiled and cool, but when he meets Death in person, he gives an enormous gasp, with the overacted line, "You're DEATH!" What's even funnier is that the character onscreen isn't animated any differently than usual, so it's all in the voice acting. Unfortunately, unlike most things Discworld, this is likely not meant as parody and is just a case of bad acting.
Lance does this painfully and in fright in Brain Dead 13 when he sees that one of the giant worms in the Spooky Silent Library has burrowed its way through his chest in one death scene.
In "The Boy Who Cried Wolf" puppet skit, the boy gasps when he sees the wolf approaching him before the wolf reveals to the boy that he isn't really evil.
In the "Gunni Wolf" puppet ski, the little girl gasps repeatedly.
In the DVD commentaries, the creators joke that Futurama has more gasps per episode than any other show ever.
Lampshaded in one episode when after repeated shocking statements, one man faints. A doctor rushes to his side and announces "This man has over-gasped!"
The eponymous Tinkerbell causes an entire group of fairies to gasp and recoil, hands rising to their faces in horror at Tink causing a stampede.
Total Drama Island is rather fond of these, either individually or in groups. It's particularly common when contestants are surprised at an elimination.
The TDA episode Oceans Eight Or Nine parodies this by showing overdramatic GASP shots of Beth, Lindsay, Justin and then Lindsay again, followed by a Shrug Take from Duncan.
The TDWT finale uses exactly the same format (list of "GASPS!" and then a Shrug Take), although the characters who perform the actions are different. The character who performs the Shrug Take (Noah) had been revealed to already be aware of the "shocking revelation" nine episodes earlier.
Spoofed on Will and Grace, when Grace snooped in Leo's bag and found a romantic letter from another woman, but wants to pretend to be shocked when he finds it:
Grace: But then he'll know I snooped. No, he's got to find this on his own. And I've got to be there when he reads it so I can act all shocked about it. Ooh, I know what I'll do. I'll do this. (does three quick gasps) No, too big. Maybe (gasps twice) Maybe just one. (does a long and wildly exaggerated gasp, with slow-mo facial expressions) Will:[beat] Grace, do you work? Or do you just spend the day practising your reactions? (Grace gives him an offended, open-mouthed look) Thought so.
Frank does this repeatedly in an episode of The Adventures of Lano and Woodley . After the third or fourth, Col tells him to stop it because there's a risk of him fainting. Frank gasps and faints. Then when he comes around, he asks what happened. Col tells him that he fainted. Guess what happens.
Lampshaded on Friends when Monica admits to an amateur cooking class that she's a professional chef. The whole class let out a theatrical GASP and Monica tells them to stop it. "This isn't a courtroom drama!"
During an All That sketch where a member of the "Cheese Police" visits the school, he finds cheese in Ms. Fingerly's purse.
Angel. Cordelia does this when spoofing the Buffy/Angel romance in "Fredless". And she actually does say gasp.
Calvin and Hobbes parodied this, during a series of strips where Calvin floats away with his helium balloon, it pops and he figures it must be a dream. To try and wake up, he looks down toward the ground and "GASP!"s repeatedly. It doesn't work.
I'm Sorry, I'll Read That Again had characters saying 'gasp' pretty often. The most notable example is probably when the entire cast, upon being told that their in-universe radio station is being closed down, react with "SHOCKED GASP!"
Parodied in Urinetown, when Pennywise reveals that Hope is her daughter, the poor react with a "Gasp." When she follows it up with the fact that she is Hope's mother, the poor give a much more dramatic, "GASP!"
Parodied in The Fairly OddParents a couple of times, at one point which Timmy's dad yells, "GIGA.GASP!!!"
In another episode Cosmo goes to a party and fabricates various achievements to impress the other guests. One of them is inventing air, which he claims the entire world must pay him royalties for every breath. Whenever the guests gasp, he tells them to pay up.
Parodied in an episode of The Oblongs where a crowd of people continually gasp until it's revealed it was just Mikey's (the ass kid) asthma.
One of the episodes of WordGirl features "gasp" as one of the words to look out for. To help show the definition of the word and make sure they could work in the word as much as possible, the characters engage in this the entire episode. It's done so much that it's taken to the point of an Overly Long Gag, and Tobey even gets fed-up at one point and shouts "Will you STOP doing that??" after the crowd gasps for the umpteenth time.
In one episode of The Penguins of Madagascar, everyone gasps upon hearing that Mort had been kidnapped. Everyone, that is, except King Julien, who momentarily forgets who Mort is, then reassures them that "I too am gasping in horror, but on the inside."
Bugs Bunny actually says "Gasp!" in the short Falling Hare, after turning around to accost the gremlin who almost tricked him into setting off a bomb with a hammer, and finding that the gremlin has vanished.