This is the Chaos God Nurgle's modus operandi: prey upon those who have succumbed to despair and cynicism, especially if this anguish comes from a hideously-disfiguring disease. His victims wallow in self-pity until they fully embrace decay and entropy, find themselves perversely enjoying the experience, and begin worshiping him. In other words, through Father Nurgle you can fall past the Despair Event Horizon and end up Affably Evil.
For another example, this is a significant chunk of the Soul Drinkers' fighting style - you break the enemy's will to fight, and then you can just kill them with ease.
The whole idea of Night Lords, whose Primarch coined the space marine battlecry "I fear no evil, for I am fear incarnate" - They are a legion of The Dreaded and just their arrival to a planet is usually enough to cause mass suicides. Then they use orbital bombardment to cover the atmosphere with ash, blocking out the sunlight, jam communication with broadcasts of tortured civilians screaming and go on their hunt.
Call of Cthulhu: Investigators (a.k.a. the PCs) wage a never ending war against the Elder Gods, slowly learning more and more of the Mythos. At one point or another, they get a view of what they're fighting, a clear unobstructed view. Those who don't Go Mad from the Revelation typically lose all motivation to fight out of finally understanding how small they really are in this fight.
It's implied in some articles about the Dirigible Engine Daystar in Exalted that the Unconquered Sun has crossed it at some point after his Chosen crossed the Moral Event Horizon and the whole world went to the dogs. This is a sign of how bad things have gotten in Creation; the cosmic embodiment of virtue is caught in a spiral of despair and denial.
Twilight 2000: Since it's about the last survivors of the last major battle of World War III, the game starts its players right next to the horizon, and it's up to them to find a way to avoid crossing it.
Being that they're both settings about personal horror, crossing the horizon is horribly frequent in The World of Darkness games — so much that many have mechanics for it.
Mages use their beliefs and sheer willpower to shape the reality around them. Pushing them over the edge and sending them into utter despair, naturally, has some terrible consequences... If luckynote for everyone else, that is, their mind (and magic) breaks and the mage becomes a Marauder, who enforces their shattered vision of reality upon the world by existing. If unlucky, they might decide that it is better for reality not to exist at all and join the Nephandi. This process involves ripping their soul inside out.
Werewolves have a word for this: Harano. It's the breaking of spirit that comes from the realization that the Wyrm has already won, and anything they would do would be utterly pointless. Werewolves who succumb to Harano lose their connection to Gaia, and worse, their connection to what makes them a werewolf, rendering them a normal human from then on. A few rare lucky souls manage to reconnect with their werewolf side, usually just in time to make a Heroic Sacrifice.
In a world full of unwilling monsters, Prometheans probably have it the worst. The universe does not want them to exist. The very earth rejects them and the people are supernaturally urged to hate them. Learning to become human is a very difficult and bitter task, but many see it as a worthy goal to fight for... But many still fall to despair and pursue a very different goal: to become monsters. A Centimanus revels in their inhuman nature and uses their alchemical powers to dissolve and disintegrate.
In Changeling: The Lost, crossing the despair event horizon is the reproductive cycle of the True Fae.