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Quoted on the main page: In Trainspotting, Sick Boy, while morally ambiguous, still has his good points. That changes when Baby Dawn, now revealed to be his daughter, dies.
In Braveheart, this trope hits William Wallace after he finds out Robert the Bruce has betrayed him. His anger immediately turns into distress and he seems to simply give up, which also later causes Robert to suffer from My God, What Have I Done?.
In Return of the Jedi, the Emperor tries his best to push young Skywalker over this, so he will turn to the dark side, by showing the Death Star is still shielded, his friends are going to die, and the Rebels are losing the battle.
The soldiers in 28 Days Later, had apparently crashed over this line before the events of the movie had even taken place.
In Lawrence of Arabia, the turning point of the movie is the capture, torture (and implied rape) of the protagonist by the Turks. The cocky, bemused Warrior Poet who believed to be invincible turns into a bitter, grim Anti-Hero after that.
In the Monty Python film Now for Something Completely Different: Parodied in the "Marriage Guidance Counsellor" sketch. At the end Mr Peuty, in despair because his wife is making out with the counselor, walks out of the office, whereupon a 16-ton weight drops on him and the caption reads "So much for pathos."
Red Dawn (1984). Things are going well for the American guerrillas until several of their group get killed trying to get a downed pilot across the front lines (the pilot also dies). Then one of their group turns out to be a traitor and has to be executed by his friends. A change in Soviet tactics leads to more of them getting killed in an ambush, so they're down to only four people. The leaders of the group, the Eckert brothers, decide to head into their Soviet-occupied hometown and go out in a Bolivian Army Ending, drawing troops into the town so the last remaining two can escape to the US lines.
The death of Ernst-Robert Grawitz by Pater Familicide, as depicted in the movie, was another example of how the fall of Berlin to Soviet forces caused many a Despair Event Horizon for Germans in the war.
In Cloverfield, right after the main character's brother dies on the bridge, you can see the exact moment that his mind breaks and self preservation stops mattering.
Gettysburg showed General George Pickett cross this after the failure of his charge.
Oh Dae-su of Oldboy crossed his DEH after learning that his lover was actually his long lost daughter, and his mortal enemy had the means to reveal the truth to her with a simple phone call.
His reaction to his DEH is hard to watch.
The President of the United States in Mars Attacks! has apparently crossed this line by the time he finally gives in to his General's request to fight back against the Martians using nuclear weapons.
In Full Metal Jacket, Private Gomer Pyle is driven into a psychotic breakdown both by the original Drill Sergeant Nasty, Gunnery Sergeant Hartman, and by the rest of his platoon, which ultimately leads to Hartman's murder and his own suicide. The moment when Pyle hit the Despair Event Horizon was probably when Hartman found a jelly doughnut in his foot locker just when things were starting to go well for him and proceeded to punish the entire platoon for it, which was then followed by the platoon taking it out on Pyle in the harrowing "blanket party" scene.
In the spirit of one upmanship and outdoing the rest of this list, A Serbian Film has Milos have one after learning that he was drugged and made to rape and kill people, including his own son, he was raped himself, and all of it was filmed for a snuff director's entertainment after which we get a Shower of Angst shot with him in the fetal position in the shower. Eventually this leads to him killing himself.
In Fourteen Oh EightMike Enslin's child daughter is brought back to life just to die in his arms and THEN THE BODY CRUMBLES INTO ASH! You can tell he is losing it as he tries to put Katy's "pieces" back together then his face afterwards is just a total emptiness inside, and the room keeps going.
The flashback scene in TRON: Legacy. Clu takes over, the Sea of Simulation is poisoned so no more life can come from it, Tron is thought dead, but it's muchworse, the Iso Cities are destroyed, and the portal back to the human world flickers out. The brash and cheerful protagonist for the first film clearly died at that point, leaving behind a hollowed-out Zen Survivor.
In Black Death, Osmund certainly suffers one of these as a result of his journey.
In Thor, this moment occurs for Loki when Odin tells him that he's actually the son of Laufey. This seems to push Loki over the edge, resulting in his badbehavior throughout the rest of the movie, its sequel, and in the subsequent The Avengers.
In Burn After Reading, Harry invokes this. Upon Harry entering the house of retired spy Osbourne Cox (as he is having an affair with Cox's wife), he panics and kills another intruder, Chad, who he believes is a spy. Cue Harry developing a Hair-Trigger Temper and distant, obsessive behavior due to paranoia and what he did.
When Atreyu finds the Rock Biter in The Neverending Story , he finds that the Rock Biter's friends have been destroyed by the Nothing, despite the Rock Biter's best efforts. Now he can just sit and reflect how useless all his strength was and wait for The Nothing to overtake him.
Rock Biter: They look like such big, strong hands, don't they?
In The Bay, Officer Jimson experiences this after performing mercy kills on a house full of people infected by isopods, then becoming infected himself.
Tony Montana crosses it in Scarface (1983) when he realizes that his impulsive protectiveness of his sister Gina caused him to kill his best friend. When Sosa's men kill Gina at the end, he proceeds to go into an Anti-Heroic RROD that (at least in this film) ends in his death.
In Speed, Jack almost crosses it when Harry dies in the raid at Payne's house.
Averted by Zod and Co. at the destruction of Krypton in Man of Steel. They're obviously crushed by its loss, but expected it and are still functioning. When the ship containing Krypton's only chance at resurrection is destroyed by Kal-El, and Zod is left kneeling in the literal ashes of his permanently dead people, he snaps and becomes a Death Seeker immediately.
Lord of War: Pay attention to Valentine's face when Yuri makes his final speech. He gets closer and closer to this over the course of the speech and finally crosses when the door knocks.
Happens to Zordon of all people in Mighty Morphin' Power Rangers: The Movie, after Ivan Ooze destroys the Command Center and the source of the Rangers' power. Though Alpha-5 gets the Rangers started on the hunt for a new power to fill the void, Zordon never really recovers, plainly stating that Ivan Ooze had won, and dies without ever finding out if the Rangers were successful or not. He is understandably very surprised when the Rangers manage to resurrect him at the end of the film.
The main character in Signsgives up his belief in God entirely after his wife is killed in a car accident. He gets it back when the "nonsense" she was saying as she was dying turned out to be important clues.
In Cube 2: Hypercube, Sasha, aka Alex Trusk, eventually gives up hope that she can escape the hypercube and completely resigns herself to her impending death. This doesn't stop Simon from murdering her in cold blood anyway.
In X-Men: Days of Future Past, when Xavier is forced to close his school after the first semester due to the Vietnam War conscription, he gives up his ambition to be a leader and protector of mutants, and becomes a self-medicating recluse.