Blood+: Saya hits it when Diva rapes and kills Riku, developing a more bitter personality and an I Work Alone mentality; several characters in-universe remark that she's lost hope.
D.Gray-Man´s Lenalee is pushed into it when Allen is wounded to about as close to death as you can get (hole in his heart, amputated left arm/innocence, Heroic B.S.O.D. from not being able to save Suman and various other injuries), she only gets to see the effects through Timcanpy and then isn't even allowed to see the presumed corpse. She understandably nearly becomes a vegetable for a while.
Allen himself crosses the horizon after these events, and he is told that he will never be able to be an Exorcist again. However, it turns out that wasn't true- Bak just wanted to make sure that Allen was determined enough to go through the dangerous process of regaining his Innocence.
Mazinger Z: The Hero Kouji almost, almost crossed it during the Mazinger-Z vs Great General of Darkness movie. After several Mykene Warrior Monsters have easily destroyed four major cities (Paris, London, New York and Moscow) they strike Tokyo. He launches Mazinger-Z to fight them... and he barely walks out of it alive. The Warrior Monsters easily rip his mecha apart and turn Tokyo into burning ruins as he is unable make anything to stop them. Back in the Home Base, he learns MORE Warrior Monsters have visited while he was away. His Home Base is in ruins, Love Interest Sayaka and victriolic best friend Boss' Humongous Mechas have been destroyed, and worst of all, his little brother Shirou got hurt cause a collapsing ceiling and is in coma. Later, Kouji was sitting on -the remains of- his room, and he cried as he said he knew he could not win and he was going to die in the next battle; poor Sayaka, who was eavesdropping, also cried as hearing him.
It was way, WAY worse in one of the first chapters of Shin Mazinger Zero, where he did fully cross it. Straight after seeing his grandfather murdering his father and murdering Sayaka after raping her, and losing one of his arms he was thrust in Mazinger-Z and his body absorbed by the machine. Turned into a raging The Berserker, he began fighting Mechanical Beasts in spite of he not even knew what they were or whence they came, and his negative emotions -pain, rage, despair, sadness, loneliness- fed Mazinger-Z until its sleeping consciousness woke up, transformed into an Eldritch Abomination by poor Kouji's despair, and it burnt the world to ashes.
Shinji crosses this line when he is forced to kill Kaworu, although that isn't actually his lowest point. That comes after he masturbates at the comatose Asuka's bedside, at which point he realizes that he has truly hit rock bottom. And then he finds out that Asuka has been chopped into pieces and eaten alive as he was too busy feeling sorry for himself to help her and he loses it completely.
Asuka is declining steadily throughout the series, specially after being on the receiving end of Mind Rape, but she gets better.
Ritsuko also hit this after realizing that she'll never be loved by Gendou (like her mom before her) and destroying the Rei clones.
Griffith of Berserk, broken in body and mind after a year's worth of torture, loses all hope of becoming captain of the Band of the Hawks again when it's discovered that he will never recover from his injuries. Then, just after he resigns himself to living a peaceful life with Casca, he discovers that she's moved on and is now in a relationship with Guts. Griffith loses it completely. This drives him to activate his Crimson Behelit, summon the Godhand, and cross the Moral Event Horizon.
Hitting one's emotional nadir this way is all but a requirement for mortal bearers of Behelits in general. It ensures that one is in the proper frame of mind to accept the offer of the Godhand to make the Sacrifice (and thus cross the bearer's personal Moral Event Horizon) to become a demon. And provided the Behelit comes into contact with blood, a member of the Godhand can also use it to manifest in the physical world, such as when Slan manifests in front of Guts using a pile of troll intestines.
Guts comes perhaps the closest that any mortal can get to the Despair Event Horizon at the end of the Eclipse, what with losing everyone in the Band of the Hawk except Casca to the demons unleashed by Griffith's acceptance of the call to Sacrifice, and then being horribly mind raped by being Forced to Watch as Casca, the only woman he's ever loved, is raped to insanity by Griffith, who has been reborn as the fifth member of the Godhand, after a furious but utterly doomed bid to save her that cost him a hand and an eye. The only thing that keeps Guts going in the face of such despair is an undying hatred for the one responsible for it all and a desire for revenge that all but consumes him for two years and nearly destroys the man that he used to be.
Ryo hits it hard in Season 2 after his loss to Edo, demotion to the minor leagues, and loss of his sponsor. This leads directly to his Freak Out and Face–Heel Turn, resulting in Hell Kaiser.
In Yu-Gi-Oh! 5D's, Kiryu was arrested and thrown into a Hellhole Prison, falsely believing his best friend Yusei had betrayed him. He suffered abuse from the corrupt guards, but was able to comfort himself by admiring his deck. Then the guards confiscated his deck and he gave up hope, leaving him open to be contacted by the Earthbound Gods and make a deal with them to seek revenge on Yusei.
It happens to Yuma in Yu-Gi-Oh! ZEXAL during his duel with III, but is subverted due to the fact that III uses a curse to steal Yuma's self-confidence, literally. Yuma is able to recover after his father appears to him in a vision, reminding him how he got the self-confidence to begin with.
The Record of a Fallen Vampire - Strauss crossed this when Stella was murdered. Then he goes on to redefine the meaning of "no hope" as he has make himself the target of hatred and is forced to fight Stella and his daughter's effective reincarnation, the Black Swan, over and over again, without being allowed to die because if he dies then the Dhampirs and the humans will probably destroy each other, and if that doesn't happen, the Dhampirs will lose their hope of being able to turn into humans.
The plot of Elfen Lied is set off by Lucy crossing the line when she finds out that the cousin Kouta is going to a festival with instead of her is a girl. Not a good reason, but at that point she snaps and starts killing on purpose.
This is actually the conclusion of a 8 to 10 years old process that began when her father abandoned her as a baby in the forest due to her cat ear-shaped horns. She was found and sent to an Orphanage of Fear, where she spent day and night tormented non stop by the other children and emotionally neglected by the staff of the facility, again, due to her horns. Then, when she finally thinks she made a friend, said friend proceeds to betray the girl's trust by telling the bullies of a puppy she was caring for; after which the bullies proceed to beat the poor thing to death right in front of her. This was the breaking point for Lucy, who snapped, awakening hervectors in the process, and slaughtered everyone in the room. Then she met Kouta, and the whole cousin issue was interpreted by the girl as another callous betrayal, driving her to a psychotically murderous rage that would become her standard mood from then on.
In Ranma ½, Ryoga has developed a ki attack that grows more powerful as he gets more depressed. In a battle where he's using this technique to solidly pound Ranma into the ground, Akane tries to cut through Ryouga's depression with a cheerful "Don't be sad! I really like you, Ryoga!... You're such a great friend!" Since Ryoga is desperately in love with her and is horrified that she only considers him a friend, this unwittingly pushes him over the Despair Event Horizon and makes his attackseven stronger.
In Monster, Johan Liebert, the title character, gains power over people by pushing them over this line, putting them completely under his control.
Paranoia Agent: This is the entire point of the series. Li'l Slugger comes to those who have reached this point, and gives them something entirely different to worry about in the form of a No-Holds-Barred Beatdown. He turns out to be the personification of this exact thing: The desire to avoid confronting the problems that drive one to despair by way of having to face a more immediate, more serious, and in this case more violent problem.
Edward and Alphonse Elric crossed this after their attempt to resurrect their mother went horribly wrong, traumatizing them both. It was only through the intervention of Roy Mustang, who told the boys that getting back their bodies was possible with the privileges of state alchemists, that they regained their will to live. Everyone else who has tried to bring those they love back from the dead with alchemy has reached this point.
Gluttony after Lust dies.
Scar crossed the Horizon in his backstory, after his friends and family were blown up by Kimblee, his brother sacrificed himself to make sure Scar lived, having a Freak Out and murdering the Rockbells in a blind rage, and then seeing his home having been reduced to rubble. The only thing keeping him going is his hatred for Amestrians, but he grows out of it eventually.
Suzaku Kururugi in Code Geass crosses this twice. First, when his girlfriend Euphemia died in the worst way possible. Later, when he nukes Tokyo under the influence of Geass. For all his loathing of the wrong means, he realizes that it's impossible for him to live according to his ideals.
Lelouch was already sitting on the fence after Shirley died in his arms and C.C. lost her memories, but he only crosses it once and for all after his attempt at rescuing Nunnallyseemingly gets her killed, the Black Knights betray him, and he just barely survives thanks to Rolo's Heroic Sacrifice. This leads a Do Not Go Gentle moment : "If anyone wishes to stop me, let them try. If there is anyone who can go beyond my despair...!".
Darcia from Wolf's Rain hits this he discovers that his lover Harmona, who has been on life support for two centuries while he was out attempting to find a cure, has been murdered while he was away from home. (And just before he could bring Cheza to help Harmona). Although we don't see the full effect of it until later, this transforms Darcia into a Nietzsche Wannabe, the Evil Counterpart, and the Big Bad.
In Black Butler, Ciel eventually reached this point after he was captured following his parent's murders.
In the anime, Jim Macken crossed it after not only he loses his brother Luke and his whole hometown, but is made into a Sex Slave by Lord Trancy. In his despair he summons Claude Faustus, kills his "owner" and renames himself Alois Trancy.
In the Mahou Sensei Negima! (first) anime, Negi himself crosses the horizon after Asuna's death on her 14th birthday, when the Deal with the Devil she made as a kid takes effect. He splinters so badly that watching it almost becomes the DEH for a few of his students.
In the manga, Negi's mother Arika found herself on the edge of it when she was about to be executed under false charges of murder and treason, as well for taking the blame for Asuna's Anti-Magic powers going haywire and plummeting a Floating Continent to the ground.
Sasame reaches this point in Prétear when he realizes that no matter how much he tries to reason with Takako, she can't come back from the dark side. So he joins her instead. It doesn't help that she nearly killed him during a battle.
Himeno's stepsister Mawata also reached the point after the face heel turned Sasame rejected her feelings in front of her family, which tops on her loneliness and hidden emotional turmoil coming from her father's death. After that, she fell into such a despair that Takako easily turned Mawata into the Barrier Maiden for the Fenrir tree, and Himeno had to work VERY hard to bring her back.
Sheryl Formossa crosses this horizon in Space Runaway Ideon, after the deaths of her sister Lin and her boyfriend Gije.
Kio finds out about life in Vagan in Episode 37. In Vagan, crossing the DEH is not an event in one's life, it's the nature of one's life. A space colony without any natural life, those living in Vagan have to get by on the scarcity of resources and money, all the while being always on the lookout for thieves. Because of the rampant poverty, most are unable to get their hands on medicine for the disease caused by Mars Rays, but even if they could it would only be a temporary measure. The disease can hit anyone from any social class and age from the impoverished such as Lu to the ruling class such as Lord Ezelcant. Conditions are so dehumanizing and hopeless, these citizens tend to lose their sense of human emotions, because loving unreservedly will only bring more pain when those people are likely to die of disease and/or poverty. Is it any wonder why so many Vagans resent the Earth Federation?
Saint Hakushin from InuYasha was driven towards the DEH as he was waiting for his death. He volunteered to be buried alive so he would become a living Buddha and help his people, but as he waited to die he realized that he really didn't want to die, and horrifyingly despaired. Naraku used this to recruit him as his Barrier Warrior.
Two of these are brought on by one plot point at completely different times. First Yuno crosses after winning the first survival game and becoming a god and realizing too late that even her new powers can't bring the dead back to life, thus Yukiteru is lost unless she creates an entire new universe and starts the survival game over. This is assuming she didn't cross it upon killing her parents. Later, Yukiteru crosses it upon the same realization, that all of the people he'd killed or helped kill under the assumption he'd be able to bring them back once he won were gone for good.
Yomi from Ga-Rei -Zero-. Yomi's adoptive father his killed by her Seishouseki-mind-controlled adoptive cousin, the cousin takes what was supposed to be her place as the family head and her inheritance, then lures her to a fight. When the cousin admits killing Yomi's father, she goes berserk and kills her. Then Mitogawa attacks Yomi, rendering her quadriplegic and mute, and she is accused of murdering her cousin. Her fiancee Noriyuki is too busy trying to prove her innocence to visit her in the hospital, his father breaks off their Perfectly Arranged Marriage because of her physical condition, and her best friend Kagura abandons her after she admits to killing her cousin. Then Mitogawa gives her the same Seishouseki, which heals her but its mind-control powers provide the extra push to send her Jumping Off the Slippery Slope and killing her former friends. Her Despair Event Horizon is such a Tearjerker that even after crossing the Moral Event Horizon she is still a sympathetic Woobie, Destroyer of Worlds.
In Spice and Wolf Horo crosses this line early in season 2, after learning that her hometown is likely gone, and has been for centuries. Cue breakdown.
In Spiral, Kanone Hilbert crosses this upon realizing that the Blade Children can never be saved. His reaction is trying to kill as many of them as he can - including all of his friends ( and half-siblings) and himself. After he is stopped, he doesn't cross back to the other side of the line: in the anime, he just leaves the country, still sulking; in the manga, the way he finally finds to "save" himself is to have a meaningful death, which will give hope to the other Bla Chil and Ayumu.
Souji Mikage from Revolutionary Girl Utena uses tactics that arguably predate those of Celestial Being, approaching young people who are in their lowest with promise of a chance to change their worlds and end what's making them suffer by defeating Utena. Specially obvious in the cases of people like Wakaba, Keiko Sonoda, or Mitsuru Tsuwabuki; in fact, he rejected Tatsuya the Onion Prince because he wasn't despairing enough. Mikage himself also went past the DEH in his backstory, and is pushed even further in the last episode of the Black Rose arc.
Prince Dios and his younger sister also crossed this in their backstories, which is what shaped them into Akio Ohtori the Magnificent Bastard and Anthy Himemiya the Rose Bride.
Shaman King: Once upon a time, there was a German boy named Faust (who was a descendant of thatFaust, by the way). He had a Victorious Childhood Friend named Elisa, a sweet and cute Ill Girl. Faust became a doctor and worked hard to develop a cure; after many years of research, he finally created the perfect medicine for her, and when she recovered they got Happily Married... and then she was shot to death by a thug. The despaired Faust began researching about necromancy to find a way to properly revive Eliza, but only managed to become a Shaman and have her as his spirit partner. Needless to say, things went bad...and specially for Faust's rivals.
Fate Testarossa had a rather nasty case of this upon learning that she was a clone, with all the memories of the original, and her mother hated her guts. Being cast aside, told she was never really loved, that her life was a lie, that she was truly despised, and told never to show her face again by the (admittedly abusive) mother she was completely devoted to will do that to you. Thanks to Arf's and Nanoha's companionship and combat therapy, respectively, she eventually snapped out of it in order to help and have one last word with her mother. Still counts, though.
Yagami Hayate in A's, when she was transported to the hospital roof to see Zafira and Vita beaten and subdued, and Signum and Shamal already gone. Then she see's what looks like her two new friends erase the first two knights and taunted about it. All after being told that she would most certainly die in a short while due to the incurable condition of her body. The people doing all this were purposely trying to set this off, in complete Break the Cutie fashion. Although she regains her composure after the initial shock wears off, then sets about restoring her family and fixing the problem at hand.
In chapter 305 of Hunter × Hunter, Gon loses himself in rage and despair after being told that Kite has been Killed Off for Real and can't be revived. When he realizes that the person who strung him along with the promise of a resurrection lied to him, he decides to sacrifice his future potential to give himself enough power in the present to crush his enemy. This is especially of note, because up until this point he had always been a typical happy-go-lucky kid.
Gon: This is it. I don't care if it's over. So I'll use everything. I'll kill you!
Jyu-Oh-Sei brings us Third/Heiser, who, after learning that Earth, which he had dreamed of visiting for his entire life, was destroyed. He collapses in despair, spends a good few minutes staring blankly at nothing, and eventually shoots himself in the head. Admittedly, his suicide was more to save Thor than a result of his Despair Event Horizon, but it still counts.
Nnoitra Jiruga hit this at some point in the past and just kept on going. He's convinced that all of the Hollows are damned and that they might as well act like it. "None of us is finding redemption, Nel."
Kaname Tousen's backstory reveals his Face–Heel Turn was motivated by this trope. The best friend he was in love with died at the hands of her own abusive husband, who wasn't punished and Tousen took up her sword in the name of justice. For him, "justice" was twisted into "revenge", not just against the man who killed her, but against the whole of Soul Society for being the kind of place where killers like that aren't punished.
Ulquiorra's backstory in UNMASKED reveals that he hit this long ago when his clan tried to kill him for being different to them. Once he escaped, he found himself in Hueco Mundo, which was just as bad as his birthplace. Isolated and unable to hear, speak, smell, feel or even eat, he crossed the despair event horizon and made nihilism his personal philosophy.
Jackie Tristan is all but stated to have crossed the DEH in her backstory. She crossed it in the moment when she found her family slaughtered and she took her brother's lifeless body in her arms. She's the only Fullbringer who was telling the truth about hating her power, and this is the reason why.
Puella Magi Madoka Magica is about young girls that approach this as they become Magical Girls, fight Witches and see how their lives are torn as a consequence, thus being very likely to become Witches themselves. The most straight up example is Sayaka Miki, who as of episode 8 crossed this due to her romantic woes, her ideals conflicting with reality, and the side-effects of Witch fighting, and becomes a witch.
Another good example is Mami Tomoe in the third timeline. Learning the Awful Truth did not mix up well with her issues on loneliness and abandonment and, after seeing Sayaka turn into a witch and having to be killed by the group, she freaked out majorly: she then killed Kyouko by destroying her Soul Gem and was about to do the same to Homura (And presumably to Madoka, before eventually killing herself), so Madoka had to mercy kill her and put her out of her misery - almost crossing it herself in the process, but she manages to come back. And then she dies.
Kyoko's Jerkassery in her first few episodes is revealed in episode 7 to be a case of despair event horizon crossed. The Pater Familicide she alone survived pushed her over in nothing flat... or did it? All hope she had before that incident gets promptly restored after Kyubey lets slip the Awful Truth, thus inverting Mami's situation in the third timeline on its head.
Homura approaches this during her fight with Walpurgis Night, realizing she's about to lose again and has to wrestle with the choice of rewinding time again, and risk corrupting Madoka's future more, or give in. Her Soul Gem starts becoming increasingly corrupted during this time. And then, in the Rebellion movie, she crosses it for real after learning that Madoka is (supposedly) not happy with having written herself out of reality and left her friends & family behind, and realizing that in the end, she failed in her mission to keep Madoka safe and happy. This results in Homura finally breaking under all the accumulated heartbreak she's built up over so much time, and she drowns in despair and becomes a Witch.
Animal X: Yuuji crosses the Despair Event Horizon when he finds out what happened to his first child: she was subjected to vivisection, died, and then her remains were kept on ice in a research facility. After that, Yuuji is quietly broken and makes remarks that show that he's reached a point where he doesn't much care if he lives or dies.
Yoji Kudou of Weiß Kreuz starts sliding towards the despair event horizon in the "Dramatic Precious" Drama CDs, and finally crosses it during Gluhen when the toll of being a Chivalrous Pervert whose job involves being a Honey Trap, romancing women for information and then more often than not either being unable to save their lives or being forced to kill them himself, finally becomes too much. At the end of the series he's come down with a case of Easy Amnesia that completely wipes out all his memories of who he is and what he's done, and he's generally considered better off left that way. That is how broken he was..
Also, Omi/Mamoru's mother Kikuno reached it in the backstory. Her husband Reiji, aware that little Mamoru was an Heroic Bastard fathered by his younger brother Shuichi, refuses to pay the ransom for a kidnapped Mamoru and the little kid was soon believed to be dead. Kikuno, already unstable for being trapped in a loveless Arranged Marriage that separated her from her beloved Shuichi, commited suicide soon afterwards.
Jose in Gunslinger Girl crosses it when he loses an eye in a botched attempt to kill the terrorist who killed Enrica, and cyborg girl Henrietta is reset to factory settings, destroying her personality so she'll never be able to take Enrica's place. By the nuclear power plant strike, Jose was so far beyond the Despair Event Horizon that after getting fragged, he has Henrietta finish the job and, as she does so, shoots her in the eye, killing her.
Most of the main plot of Trigun that made it into the anime (the manga had all this backstory stuff and Knives going One-Winged Angel and staying that way for over a year while he slowly killed off the human race) was a Break the Cutie-slash-Break the Stoic plot aimed at pushing Vash over this, probably in hopes of inducing Face–Heel Turn, but possibly just to punish him for being a disloyal brother. It works insofar as he is pushed past his (admittedly impressive) limits on a couple of occasions, which variously result in a two year retirement and brief catatonia.
Meanwhile, the greatest one in a series full of them is when Vash and Knives were one year old, and foundoutaboutTesla. Two boys—physiologically around eight—read the documentation and looked at the corpse, and then shut themselves up in the lab where it had happened and didn't move for over a week. Rem didn't manage to break in to save them until after they'd passed out half-dead from thirst.
And then, Vash tried to kill himself with a fruit knife at the first opportunity, and laughed somewhere between hysteria and mania upon thinking he'd accidentally killed Rem when she interfered. Knives, on the other hand, pretended to have Easy Amnesia and then proceeded to methodically enact a plan to Kill All Humans. The kicker is that Knives was always the nicer, more trusting one, before.
Legato Bluesummers appears to have spent enough of his childhood in this that when he started developing his mind-control powers he prioritized 'killing everybody connected to my life' over getting away, and was consequently in the process of being raped to death when Knives happened to come along and slice up the building and...save the day. And not kill Legato, and ask him his name. Nicest thing that ever happened to the kid.
Several of the Gung Ho Guns have this in their backstories. One in the manga notably is in this omnicide gig because he was a deformed beggar in July when Vash inadvertently blew it up, and the one good thing in his life (a lovely waitress who was kind to him) was killed, and his whole life since has been Training from Hell to get revenge on Vash.
In chapter 115 of Medaka Box, Zenkichi collapses on his hands and knees in despair after he realizes he isn't special to Medaka anymore. Chapter 116 reveals that Ajimu masterminded this Despair Event Horizon to make Zenkichi receptive to joining her Flask Plan as its first test subject.
In Chobits, We see that Freya has crossed the horizon when she begins to physically malfunction from the incredible emotional strain of being in (and being unable to tell anyone about) an unrequited love situation. In the anime, we are even shown the exact moment this happens. Depending on whether one is reading the manga or watching the anime, she is either Driven to Suicide or dies from despair, respectively.
In Magic Knight Rayearth, Princess Emeraude plowed through this when her beloved Zagato was killed by the Knights, believing him to be the Big Bad. She already was unstable after keeping her love for Zagato bottled up, seeing that since she couldn't devote herself 100% to Cephiro, her Pillar work wasn't effective as it should be, and being kidnapped by a desperate Zagato who doesn't want the Knights to release her from Pillar-dom through death, and in the anime giving her brother amnesia at his own request... and once Zagato kicked it in battle, the poor broken person reacted by unleashing her powers on the Knights and trying to kill them, calling them out on his death. The girls have to give her an I Cannot Self-Terminate, and the Downer Ending of the first season kicks in.
In SHUFFLE! Kaede lost the will to live following her mother's death but Rin managed to snap her out of it... by making her believe he was the reason she died. She snapped out of it, but her attitude is now towards taking out all of her hatred out on him. She then suffers another one when she remembers it was because of her that her mother came home earlier and took the flight, now blaming herself for both of her mother's death and all the pain she caused Rin.
Sasuke Uchiha spent a big part of his life on the verge one, but completely crossed it after Itachi died and Tobi reveals to him that Itachi had actually killed their clan because said clan was planning a coup, which would've led to a civil war and likely a world war, and since Itachi couldn't bring himself to kill his little brother he became a Stealth Mentor in the hopes that Sasuke would kill him, which would avenge their clan and make Sasuke a hero to the village. Sasuke reacts... poorly to this.
Naruto nearly crossed it twice: The first time, when it seemed Hinata was killed by Pain, right before his very eyes. Luckily, his dad brought him back. The second, when Neji sacrificed his life to shield him and Hinata from a fatal attack from Obito. Obito decides to take advantage of this opportunity giving him Breaking Lecture about his naivety and inability to protect everyone. Naruto starts hesitates but Hinata pulls herself together and manages to snap him out of it before he falls into despair.
Tobi aka Obito Uchiha crossed it when his team-mate Rin committed suicide freehand of his best friend who promised to protect her at any cost. Unlike Naruto, however, no one helped him, he didn't come back, and took itout onthe whole world. He would likely have also committed suicide instead if Madara hadn't arranged the situation and put in a safeguard to prevent it.
Kazemaru after The Genesis decimated Raimon and injured Fubuki, to the point that he actually left Raimon.
Unexpectedly Endou. After Kazemaru left Raimon, Endou lost all of his enthusiasm for soccer.
Fubuki crossed it when Desarm effortlessly stopped Eternal Blizzard, after that incident he couldn't dare himself to touch another soccer ball.
In Life Is Money, this is used as a weapon because any character whose anxiety gets high enough dies.
At the climax of the sixth volume in High School D×D, Issei crossed it when he thought Asia was gone for good when she disappears from the group just after rescuing her from becoming a nuke that would kill all the devils in the Underworld. He then transforms into a monstrous form called Juggernaut Drive that gives him immense power at the cost of his lifespan. Fortunately, he snaps out of it.
Smile Pretty Cure! actually invokes this trope. Big Bad Pierrot is able to get ahold of the storybook telling of the team's history and splotches down some of his Bad End Ink on some of the unwritten pages, plunging the girls into despair. Candy's able to snap them out of it, though.
Haruka suffered a lot in Kotoura-san's Downer Beginning, but it was stray cat incident (when a lonely Haruka desperately latches onto a stray cat she finds in a park, caring for it because she can't hear its thoughts and believes it is her only friend, only for it to be taken to a shelter - effectively a death sentence in Japan - by an insensitive old woman) that made her to decide she is indeed a monster (as people already said about her) that would bring doom to every living being that she cares about. From that point on she became a complete Broken Bird and wore a Jerkass Façade so that nobody would care her and vice versa, until Manabe broke her shell.
That wasn't the first time. The first time was after Sachi died in front of him because he failed to warn his friends about a trap and he wasn't able to save them. A few months later, he gets a Hope Spot in the form of learning of an item that can revive the dead, only to have his hopes crushed when he obtains the item and finds out in only works within ten seconds of the target's death. Only receiving a Christmas Card that Sachi had sent shortly before her death is able to snap him out of his despair- she figured she wouldn't survive until Christmas and that Kirito would blame himself for her death, so she recorded a message thanking him for the time they had together and for giving her joy and hope, as well as telling him not to blame himself for her death.
Fai in Tsubasa Reservoir Chronicle seems to have made it his hobby to find new DEH's and falling off them. Most notably in Celes when Ashura drives an icicle through Kurogane's chest and he finally snaps and tries to kill both himself and Ashura in one fell blow. Thankfully, Kurogane gets better.
In Hell Girl, most people who call upon Ai to send their tormentors to Hell have crossed this, most often at the moment they decide to pull the red string.
First off, Saten has one as she finds out the side effect of using Level Upper: falling into a coma that no one has come out of.
Second is Mikoto's, which is much, much deeper. She's trying to stop the Level 6 Shift experiments, and after pushing herself to her limits and still failing, she comes to the conclusion that the only way to stop the experiments is her suicide.
Reiner appears to have gone over it after revealing his true identity. He clings to the idea of completing his mission in order to function but is resigned to dying as a mass murderer.
From The Seven Deadly Sins, this is what drove Helbram into becoming an Ax-Crazy human massacring Faux Affably Evil villain. After he and a few of his fairy friends were captured by greedy humans wanting to use their wings for medicine, and after witnessing firsthand his friends get their wings ripped off, he loses all the respect and fascination he once had for humanity. So much so that he can longer stop himself from killing humans regardless of his own desires.
Many of the past victims and Sympathetic Murderers in Detective Conan are people who, for one or another reason, have crossed the DEH and either died or became killers as an effect. The case involving the Star-Crossed Lovers Hideomi and Miyuki is a very blatant example: the first had lived in the fence after a Deadly Prank caused him to be scarred and killed Miyuki's parents, but crossed it when Miyuki fell in love with him despite his crime, which caused him to commit suicide; the second went past the DEH fence when she found Hideomi's corpse, pushing her to murder the other person involved in the Deadly Prank by using said person's own plans against him, and then to try commiting suicide so she and Hideomi could be Together in Death. (She's stopped by Conan, and is soon screaming and crying about how badly she wants to die, until Hideomi's father gently talks her out of it.)
King Piccolo plunges the world into utter despair not once, but twice after he took over the world. It was the Darkest Hour of the original series.
After Frieza mortally wounds Piccolo, murders Krillin, and threatens to kill Gohan, Goku crosses over the despair line. That despair, however, quickly turns into uncontrollable rage.
When Cell returns after Goku made his Heroic Sacrifice to stop him from blowing up the Earth, he kills Trunks and badly wounds both Vegeta and Gohan. After declaring that he will destroy the Earth and the entire solar system, all the Earth's warriors completely give up. It takes Goku talking from the grave to get Gohan to make one last stand against Cell.
Both Vegeta and Goku fall into this after the Earth is destroyed by Majin Buu.
Miki undergoes one in chapter 7 due to being the Sole Survivor of her group. She is completely isolated from anyone and is stuck in a storage room. She refuses to just sit around and die but the loneliness and boredom is getting to her. The other girls rescue her within a few chapters.
Yuuri hit this line in chapter 27 after a rescue helicopter crashes and then bursts into flames in front of the school. She's usually a calm Cool Big Sis but she completely snaps afterwards. Her emotional barrier goes down once Yuki is out of earshot. Even after she calms down she is snappy at Yuki which is unusual for her. Yuuri isn't the same after the events, even after she seems to recover, as she begins undergoing a Sanity Slippagewhich leads to her hallucinating a stuffed animal is her little sister.
In Fist of the North Star, Kenshiro was left with little purpose in life after the supposed death of his fiancée Yuria and things don't always go smoothly despite his overwhelming power, but he fights on out of a desire to help the good people. The first series ended with Kenshiro learning Yuria was actually alive, but also sick from radiation. As shown in the Last Piece interquel, her definitive death brought Ken into a deep depression and he couldn't muster the will to save his village from yet another army of bandits. The young son of Juza then decides Kenshiro has already given too much and takes up the torch along with Cool Horse Kokuoh to fight off the marauders, but fails and is killed. Seeing a now one-eyed Kokuoh bringing his corpse back while still requesting help finally snaps Kenshiro out of his funk. He thrashes the bandits and resolves to never fall that low again.
In Uzumaki, Kirie can't exactly be said to lack resolve and an incredibly strong will to survive. After losing literally everything, though (including her home, her family, and finally her boyfriend) she reaches the point where she is unable to take the emotional torment anymore and just lies down next to Shuichi, joining him in the Spiral.
In Side:Despair, Hajime crosses it after his attempt to investigate his friend's murder gets him thrashed by the school's security guard, then given a Breaking Speech about just how worthless and replaceable a Reserve Course student like him is. Given that he's been struggling with these exact same feelings for the past few episodes, this utterly shatters him and is the deciding factor for his decision to go be transformed into Izuru.
Later in Side:Despair, Class-77 B crosses it in unison when they're Forced to WatchChiaki being tortured to death.
Chiaki herself seems to cross it in her final scene; after the Trauma Conga Line of losing her boyfriend, being betrayed by her teacher, realizing she inadvertently lead her classmates to their doom, being horrifically tortured, and being left to bleed to death, she just breaks down in tears sobbing about how she doesn't want to die.
Subverted with Izuru. Junko thought she'd pushed him over it when she told him exactly how, while he might save the world, there'd be no one to save him from his burdens, and that the world would remain meaningless and boring to him unless he joined her in bringing despair. In reality, Chiaki's final words to him gave him the realization that maybe despair wasn't the only path left for him, and he left Junko's service shortly after.
At the end of Side:Future, Ryota hurtles past this upon realizing that the Future Foundation's head, his mentor Tengan, was corrupt all along and instigated the Killing Game. Combined with his past trauma from inadvertently helping Junko destroy the world, he completely gives up on hope for humanity and decides the best way to save the world is with mass brainwashing.