In the backstory, Kirei Kotomine crossed the Despair Event Horizon after the death of his wife Claudia, abandoning his attempt at living a 'good' life and fully embracing the fact that he can only feel happy through hurting others.
Archer crossed the Despair Event Horizon after being betrayed by everyone he ever knew and finally, his own ideals. This leads him to try to kill Shirou, his past self and living embodiment of his misguided ideals, at any cost. In the end, he is beaten by Shirou despite being the superior opponent, his acknowledgment that those beliefs were not so mistaken after all.
Finally, Shirou goes through this in the Heaven's Feel route. He gives up on his ideals to save Sakura, who happens to be eating people and is about to turn into a world destroying monster. He's not one to sit around, though, so he just takes up another cause with gusto.
He permanently crosses the horizon in one bad ending when Rin kills Sakura. He abandoned his dream to protect Sakura and failed to do even that, leaving him with nothing to live for.
In EP7 it's revealed that Kinzo crossed this line some time after his secret lover Beatrice Castiglioni's Death by Childbirth. As for how he crossed it, it turns out that he eventually raped their illegitimate daughter Beatrice Ushiromiya, since she grew to look so much like Beatrice Castiglioni that Kinzo deluded himself into thinking that she was her mother's reincarnation.
This is hinted to have occurred to Sayo Yasuda, alias Shannon, Beatrice and Kanon after realizing that Battler would come back to the island exactly the same year George was going to propose to Shannon. S/he instigates the murders that occur on the island and throws away everything for a chance of a miracle and make Battler realize his sin.
Kohaku of Tsukihime also crosses the Despair Event Horizon after being raped several times by SHIKI and his father in order to stop their inversion impulses and becomes utterly broken, as revealed in the Far Side routes.
Keisuke's death in Togainu no Chi is this for Akira on Shiki's route. Even though he still puts up a bit of a fight against Shiki, it's nowhere near the same defiance he had before. He also doesn't care whether he lives or dies and decides that whatever happens to him is punishment for killing Keisuke.
Thee Bad Endings of Katawa Shoujo imply that, if the player takes the wrong choices, the girls might reach this extreme. Some examples are: Rin's bad (where she and Hisao have a terrible fight and she ends up alone in her atelier) and neutral (in which she accepts a scholarship in Tokyo but at the cost of breaking all bonds with Hisao and everyone else) endings, Shizune's bad ending (with Misha reaching it first via asking Hisao to sex her updue to her hidden loneliness, and then Shizune following when she breaks up with Hisao thinking that she is ruining his and Misha's lives — and the last view of her that he has is Shizune sitting all alone in the stairs), and Hanako's bad ending (with her blowing up at Hisao as she realizes that he and Lilly only view her as a child whom they have to protect, thus breaking her already smashed self-estreem and making her splinter)
Aso, if the beta that was leaked a while ago is to be believed, Hanako's Bad Ending would've had her killing herself in front of Hisao (via jumping in the path of a train after their last talk) instead of blowing up at him. And for worse, Shizune's path would've had two possible DEH crossings: Misha throwing herself in front of a car on Shizune's range of view after the Sex for Solace scene... followed by Shizune falling into catatonia, with two possible options for Hisao-as-the-player: helping her regain the will to live, or being unable to stop Shizune's Death by Despair.
Dangan Ronpa's Monokuma is all about bringing DESPAIR to the world, and pushes the buttons of his victims in order to try and drive them over this and to murdering one another. (And personally executing them if they do kill and are caught.) He succeeds in the case of Sayaka Maizono, an Idol Singer with hidden insecurities who freaks out massively after she's shown a video where she's told that, if she doesn't "graduate" of Hope's Peak via killing others, she'll be abandoned and forgotten; and is this close to succeed too with Aoi Asahina, a sweet sportswoman whom he manipulates into getting everyone framed for the murder of her best friend Sakura. The other students manage to bring her back.
Kiyotaka Ishimaru comes damn close to the DEH after the execution of Mondo Oowada, his best friend. He is murdered shortly afterwards.
The Good Ending of the game is all about Naegi picking up his Messianic Archetype ID and actually keeping the remaining students (Asahina, Kirigiri, Togami, Fukawa and Hagakure) from reaching the DEH at the hands of Monokuma... or better said, Junko Enoshima, who is the one behind him. He actually screams "YOU MUST NOT LOSE HOPE!" at them while Junko eggs them to cross the DEH. Alternatively, in the Bad Ending, after Kirigiri's execution the five remaining kids (or four, since Fukawa has died) have crossed it, but they're now living peacefully in the Gilded Cage that Hope's Peak is for them, alone in the world save for themselves and their children...
Taken Up to Eleven in Super Dangan Ronpa 2. It's revealed that 15 of the students (Chiaki is excluded because she wasn't a Hope's Peak Academy student) had all crossed both the DEH and the Moral Event Horizon before the events of the first game when they joined Ultimate Despair, all thanks to Junko Enoshima. In fact, the students were so far beyond the DEH and MEH that they all had to be placed inside a virtual reality program in order to overwrite their memories of Ultimate Despair. Unfortunately, Junko is still able to spread her despair inside the program, and temporarily pushes the surviving students past the DEH again in the climax. She's only thwarted when Hajime overcomes his after a Rousing Speech from Chiaki encourages him to overcome their terrible past and write their own futures.
Little Busters!: Riki passes this at the end of Rin's route in the timeline where he and she run away together. Rin's been taken away from him forever, passing a Despair Event Horizon herself offscreen, and his best friends and only family - especially Kyousuke, whom he used to look up to more than anyone else - have proven themselves untrustworthy. Thankfully, Kyousuke is able to reset this timeline, though the consequences were so extreme that it has much a much bigger effect on later timelines than any other.
Not to mention that the whole plotline happened because Kyousuke was convinced that the bus crash killing him and the others would push Riki and Rin over it, such that he was willing to do anything at all that might make them strong enough to withstand it and not give in to despair.
Higurashi: When They Cry: Rena crossed this in her backstory, after her mother revealed she was leaving her father for another man (whose child she was carrying), and after a subsequent (heavily implied) rape attempt by three of her male friends, leading to a berserk rampage. This leads to an attempted suicide.
She also appears to cross one in the Atonement Arc, around the time she starts believing her friends - specifically Mion - are working against her. Unfortunately, it serves to fuel her growing madness.
Rika and Hanyuu are revealed to have spent the majority of the story this way; after centuries of failure, Rika eventually gave in to her fate of dying in June 1983, and stopped trying to fight it.