Stress comes in many shapes and forms. You almost kill a patient on your first day as a doctor. You find out your parents were never in love. You discover the world you thought you knew was never real. Your intestines are falling out of your belly-wound. Your opponent is just that terrifying. Conflict creates stress, and, on television at least, stress creates vomiting.
Note that no nauseous event or spectacle need occur to precipitate a Stress Vomit, though a sufficiently gory and horrific sight will most certainly do it for some people. If any event or revelation causes high levels of anxiety in a particular person, that person will lose their lunch.
This is Truth in Television; some people do respond to anxiety with retching (dry heaves) or actual vomiting, and in some cases it happens repeatedly, in a condition known as Cyclic(al) Vomiting Syndrome (CVS).
Super Trope to Vomiting Cop, since cops are human too (well, mostly or formerly).
In Tengen Toppa Gurren Lagann, Simon's robot, the Lagann, starts vomiting Spiral Energy during the more stressful moments Simon goes through after Kamina's death.
In Neon Genesis Evangelion, Episode 20 generates quite a lot of stress and subsequent trauma for Maya Ibuki, the sequence beginning at the start of the final third of the episode: first, Maya safely presumes that both she and her colleagues will either be eaten alive or disintegrated; then, hope she'd rejected resurges when Shinji returns in EVA 01 to save them from the beast; then, it dies when EVA 01's battery power empties; then, it returns when EVA 01 reactivatesto protect it's pilot; finally, she witnesses EVA 01 overpower the beast and then devour it. She spews.
Soul Eater has a comedic example in the anime. Maka's team loses a game of basketball, so as a forfeit she has to offer to spend the weekend with her Bumbling Dad. He's so happy at the prospect of unexpectedly spending time with his sort-of-estranged daughter he vomits.
Near the end of the Bokurano manga, Jun Ushiro, faced with the extremely unpleasant task of killing everyone in his final opponent's universe one by one until he kills the final enemy pilot (whose death will result in his universe being destroyed and Jun's being saved), vomits from the stress.
Elfen Lied: Lucy tosses her cookies at the height of her emotional breakdown as a child: specifically when she finds out Kohta had lied to her about his cousin's gender.
Karasawa of Daily Lives of High School Boys had one during High School Girls are Funky: Archdemon when he was reminded of Habara. Fanon takes it to be a permanent trait, seeing he might actually be phobic to her.
Mary Jane has done this at least twice in the Spider-Man comics:
Once when Peter and Felicia told her their plan to find the kidnapped Aunt May involved freeing Norman Osborn from jail.
In The Rock, Stanley Goodspeed throws up when he's recruited to be part of the rescue mission, and told the full risks of going in.
Saving Private Ryan had some of the soldiers in the landing craft losing their cookies on their way to the D-Day landing. Though the sea travel likely didn't help, anxiety about invading France to retake it from the Nazis doubtless contributed to their nausea. This was parodied (along with the rest of the landing sequence) in Conker's Bad Fur Day.
The Matrix. While in virtual reality Neo learns that his entire previous life has been an illusion and most of the human race is enslaved by the machines. He can't accept this, and after returning to the real world he throws up on the deck of the hovership.
The Bourne Identity. Already in shock from the Mood Whiplash of events after Castel attacks them, Marie throws up as she's herded out of the apartment by Bourne and sees the headshot body of the concierge.
Serenity. While on the planet Miranda, the crew learns a horrifying truth about the origin of the Reavers, causing River Tam to throw up.
Played for Laughs in Pitch Perfect. Aubrey throws up over the entire audience during a group performance. Later on she does it again as part of a particular hilarious argument.
In Killer Elite, Danny's team hires Jake, an inexperienced small-time criminal who promptly vomits after shooting both an enemy agent and fellow team member Meier in the head in a fit of panic.
In Requiem for a Dream, we get this twice. The first time is after Marian sleeps with her therapist for money. The second time is while Tyrone is making prison food while the security guard mocks him (although in his case, he was addicted to heroin, so that might've had something to do with it.).
In The Princess Diaries, this is used early on as evidence of Mia's social awkwardness. When she has to present her side of a debate in front of her class, she ends up bolting from the room to throw up. She brings this up during the rambling prelude to the speech she makes at the end of the movie, prompting the reporters present to nervously back away a little.
In Any Given Sunday Willie Beamen's nervousness at being sent into his first gamenote after both of the more experienced QBs on his team are injured causes him to throw up in the huddle. In later games, he's seen throwing up on the sidelines before taking his first snap.
In Rush, James Hunt is seen throwing up before races.
Pro skater Mike McGill mentioned in the The Bones Brigade autobiography that he threw up during a competition in Texas behind the ramp due to the stress of losing the contest. This was back in the time when skateboarding was all about the contests and if lost, the skaters will lose their pro status.
In Deryni Checkmate, Sean Lord Derry is on a reconnaissance mission for Morgan in the town of Fathane when he's accosted in an alley by two men who try to drug him. He kills one of them outright in his fight for freedom, but he has to slit the throat of the injured partner before the fellow comes to and raises the alarm. Derry leaves the alley and resumes his drunk act, retching in a nearby gutter. Passersby thought him simply drunk, "but Derry knew better."
After his forces defeat those of Sicard and Loris at the climax of The King's Justice, Kelson goes in search of Duncan McLain. On seeing the extent of Duncan's injuries, Kelson is so lightheaded he must put his head briefly between his knees. When he assists the men treating Duncan by using his powers on Duncan's mind, the memories of Duncan's torture and near-execution combined with his present pain are too much for Kelson; Morgan takes over, and he is violently sick before passing out from exhaustion.
In the epilogue to The Quest for Saint Camber, we learn that the execution of Kelson's cousin Conall for treason went badly, partly because the executioner was unnerved at having to kill a Haldane prince, and partly because Conall himself flinched: "It had taken two more blows to end the matter—though at least Conall knew nothing after the first—and Kelson had been violently and wretchedly sick as soon as he was out of public view."
In Going Postal, after Moist von Lipwig kills an assassin in self defense (which results in Ludicrous Gibs), the text notes that it would be the perfect time for a Bond One-Liner. Instead, Moist just becomes noisily sick.
Subverted in The Turkish Gambit, when Varya throws up after spending days bandaging the wounded and, to top it off, learning that her fiance attempted suicide. She thinks that it's just stress but it turns out that she contracted typhoid fever, putting her out of commission for weeks.
Late in Lynn Shepherd's 2012 novel The Solitary House, protagonist and investigator Charles Maddox finds his housemaid vomiting in the kitchen, and he learns from another servant that she had been accosted while buying provisions at the markets and a package was added to her basket. The package proves to contain the decaying remains of the little finger from Charles's right hand, which had been forcibly amputated in an attack on him several days previously.
In Tamora Pierce's Song of the Lioness, Alanna throws up after killing for the first time, and after helping the wounded in the field hospital. When she says it makes her feel like a sissy, Jon confesses that it happened to him too. It happens again in the final book when she has to kill her friend and Rival Turned Evil Alex.
Live Action Television
M*A*S*H: After B.J. first arrives in Korea, he faces a young Korean girl injured in a minefield, pinned down by guerilla sniper fire, and having to assist foot soldiers under mortar fire, all before he even got to camp; at one point, when he sees how badly a soldier had been wounded (and killed) by mortar fire, and the situation finally sinks in, he crawls over to a thicket of tall grass to vomit, while Hawkeye holds his head for him.
Grey's Anatomy. Episode 1: Meredith almost kills a patient through inaction. After a stressful moment that patient is saved and Meredith endures the scorn of her attending physician and her resident. She rushes out of the hospital into the pouring rain to empty her guts tastefully into the bushes.
"Mutiny": A sailor from Hornblower's division falls down from a mast and gets smashed on the deck. His blood splatters on Midshipman Wellard, who promptly throws up.
Horatio is known to suffer from seasickness when he comes aboard any ship before a cruise after being ashore. In "Duty", he's heard vomiting in his cabin; however, it happened just before his wedding and he was having cold feet, so his stomach might have been unsettled by being nervous.
Sex and the City: Carrie throws up in the sink when she discovers Aiden's engagement ring. She finds it ugly and she's not very certain about their relationship. A reaction this strong surprises her though.
Midsomer Murders: one character immediately starts vomiting when she learns the guy she's been banging through the whole episode is actually her nephew. He doesn't really react to that, given that he also just learned he's the product of Brother-Sister Incest.
In a Flashback episode of The Mentalist showing Jane's first case with the CBI, before he even becomes an official "consultant," he vomits after seeing his first dead body.
On Night Court, Christine is so stressed out over whether she should accept a marriage proposal that she throws up in Dan's briefcase - we don't see it, but Bull figures out how to use his instant camera right then and captures it.
Danger: UXB. Lieutenant Ash throws up after defusing his first unexploded bomb.
Game of Thrones. As Stannis' invasion fleet sails up Blackwater Bay to attack King's Landing, a soldier in the hold throws up into a barrel already full to the brim with vomit.
In Jacksfilms' "Dubstep Solves Everything" video, Jack's convulsing to his own dubstep noises makes the girl he's coming onto puke in distress and creeped-out-ness.
In The Awesomes, Muscleman reveals that he rarely freaks out due to long experience with the bizarre things that happen around superheroes, but when he does, he vomits. The episode then has him vomit repeatedly.