Justified and deconstructed in Berserk, as it highlights another consequence of Casca's rape trauma after the eclipse. Casca was mentally traumatized to the point where she was reduced to an infantile, almost animalistic state of mind. Therefore, Casca really has no logical drive and relies on her instincts to protect herself, so when someone poses a threat to her, she reacts violently. After Guts almost rapes her but ends up biting her instead, Casca's natural reaction is to stay far away from him at any means necessary (even jumping off a ledge) and to growl whenever he comes into her vicinity. This has taken its emotional toll on Guts, who is truly ashamed at what he did to her but desperately yearns for her emotional and physical affection. Making the situation worse, his nasty Enemy Withinwants Guts to rape and kill her. However, some people, characters (like Farnese) and fans alike, don't understand the extent of Casca's condition or backstory and think that her current behavior toward Guts is idiotic, irrational, and selfish.
Turns out that the only main female character who doesn't get hit by this trope is a prepubescent girl.
In Puella Magi Madoka Magica, Kyubey only makes contracts with girls because of this trope. Girls tend to be more emotional than boys, and they're more likely to wish for something that they think will get them what they want instead of wishing for it directly. And that suits his needs just fine: the sooner they fall to despair, the faster they become Witches, and all the more energy for him to harvest.
The gag is recycled in Airplane II: The Sequel when the same woman testifies on Ted Stryker's behalf in a Kangaroo Court — the memory of her hysterics sends her into a fresh episode of hysterics, which prompts the members of the court to line up to beat it out of her.
Airport '77 where Lee Grant, hysterical following her husband's death, attempts to open the plane door while it's submerged in the ocean. However, she is stopped by the flight attendant who is also female, so it could be considered a one off. The Airport series, itself, actually had many female characters who remained in control and were instrumental in resolving the crises. There were also cases of panicking men, as well.
Lambert (Veronica Cartwright) in Alien. She's by far the most terrified and emotional member of the crew, and completely freezes up when the Alien confronts her.
Jaws 2. After the shark attacks them, one of the female teenagers eventually goes hysterical, screaming like crazy and having a panic attack when their rafts get stuck at the bottom. Another one tries to shut her up by shaking her violently, but is told by his friends that this won't help. Not all the women are like this, but it stands out because by contrast the guys are all portrayed as practical and goal-oriented, and none of them breaks down to the same degree. Even the much younger Michael holds it together better than her, who by all accounts has far more right to be freaked out due to being a kid.
In The Fugitive, as the US Marshals conduct a raid on a home looking for an escaped prisoner, his girlfriend begins shrieking and screaming. She stops briefly when he's shot, then starts up again almost immediately, leaving the unsympathetic, fed-up Gerard to point his gun at her and snap at her to "Shut up"
In Blue Jasmine, this is the essential character trope of the lead character who becomes more and more emotionally unstable until the end when she is reduced to a homeless tramp babbling to herself about her troubles.
The narrator of The Yellow Wallpaper was diagnosed with hysteria. The whole point of the work was that isolating and babying women who became mentally ill was not the way to treat them; the narrator doesn't start out insane — at worst, suffering from postpartum depression, but she's slowly driven to madness after being more or less imprisoned in order for her to rest.
The wandering womb diagnosis gets direct mention as "a classic case of hysteria" by a doctor in one of the Marcus Didius Falco novels (set in 1st century Rome), along with Helena Justina's utter contempt for this particular brand of medical theory.
In Murder on the Orient Express, Mrs. Hubbard goes through this a few times. First is when the supposed murderer escapes into her room after murdering Mr. Ratchett, then when she discovers the murder weapon in her sponge bag. It's an act.
Sue Bridehead in Jude the Obscure appears to be a walking bundle of neuroses who is nonetheless trying to live life as an enlightened, liberated woman. It doesn't end up working for her.
In Charlie and the Chocolate Factory, the mothers of the four brats each fall into panicky screaming as one by one their offspring meet various absurd fates in the factory, though both Violet and Mike's dads are similarly upset. (In the case of Veruca's parents, Mr. Salt is deliberately presented as ridiculously calm about her potential fate compared to his wife.) Two mothers are usually Demoted to Extra and/or Adapted Out in adaptations, and the remaning moms sometimes get more rounded personalities in the bargain (Mrs. Beauregarde becomes an icy Stage Mom in the 2005 film and averts this trope, and Mrs. Teavee's anxious Stepford Smiler nature in the 2013 musical stems partially from her having to deal with an Enfante Terrible son). Still, Mrs. Gloop always comes off as this when her son goes up the pipe, owing perhaps to their limited stage/screen time (they're the first tour group to be eliminated) superseding in-depth character development, and Mrs. Teavee is definitely this in the 1971 film.
Live Action TV
House had a mass hysteria case where the normally competent Dr. Cuddy was struck hard by this trope. Like the ass he is, House told her that her gender made her more vulnerable to it than him.
Dr. Janice Lester, a villain-of-the-week from Star Trek: The Original Series was one of these. She quickly went insane when put in command of a ship, and broke down sobbing into her male assistant's arms at the end of the episode. She was also, at one point explicitly described as "red-faced with hysteria."
From "Wolf in the Fold":
Kirk: All right, Mister Spock, what do we have? A creature without form, that feeds on horror and fear, that must assume a physical shape to kill.
Spock: And I suspect preys on women because women are more easily and more deeply terrified, generating more sheer horror than the male of the species.
The trope is alive and well in Boardwalk Empire, at least when it pertains to extras. If somebody gets killed and there is people to see it or find the body, you can guarantee that there will be a woman screaming, while all the men remain silent or are, at least, far less noisy.
A lover of a victim in The Closer, was this in spades. The second that she saw the body, she started screaming hysterically. She kept on screaming causing the investigators to wear earplugs around her.
True Blood's female characters are prone to emitting high-pitched screams whenever they find a body or something like that. Not even screaming "Help!", just screaming. None of the male characters do this.
Mary Warren in The Crucible is a deconstruction. Because other characters know she is emotionally fragile, both men and stronger women bully her, knowing she won't stand up for herself.
Inverted in Quest for Glory III. Tarna, land of the liontaur people, though a monarchy with a king, has a council of lawmakers made up entirely of women because men are seen as too emotional to make government decisions.
Dead Space's female population was almost entirely these or Laughing Mad women. Justified by the fact that enemies hunted down, killed, mutilated, and revived you as one of them.
Implied in Valkyria Chronicles. By the end of their respective character arcs, the three highest-ranked women in the game are too ruled by their emotions to make sound judgements, and they self-destruct or not according to whether their male love interests care enough about them to stop them. In each case, the woman in question had been otherwise calm, collected, and competent leading up to this point.
Alicia spends the second half of the game building up to an emotional meltdown, but main character Welkin (and the rest of Squad 7, really) brushes off her cries for help until she has a literal meltdown, at which point he calms her down with a hug and an engagement ring. Apparently she wasn't worth listening to before she tried to kill herself in the most bombastic and destructive way possible, and afterward, all she really needed was a husband and a baby.
Varrot's entire military career hinges on her ice-cold seething desire for revenge for her murdered lover. When she gets the chance, Largo talks her out of it, and they later marry and return to his farm.
Selvaria. She kills herself because Maximillian orders her to, and although she realizes he's only been using her as a weapon and so sabotages her Suicide Attack by sparing the heroes, she goes through with it because she loves him.
Played for Laughs in Girl Genius. One of the Jägermonsters is ordered to accompany Agatha home, after she was expelled from the university, and she thinks that it will eat her as soon as no one can see them. She proceeds to scream hysterically for several panels, while the Jägermonster tries unsuccessfully to assure her it has no intention of eating her. She finally shuts up when it considers eating her just to get some quiet. (After Agatha Took a Level in Badass, she very much averts this trope.)
Mocked in, of course, The Simpsons. Marge foils a burglar and Homer arrives far too late (being unable to maintain the same running speed as Marge). Marge says how exhilarating it was, to which Homer responds that it's always exhilarating to watch the police get their man and save "a hysterical woman."