In White Wolf's Werewolf: The Apocalypse, Werewolves can go into a state of deep spiritual sadness called Harano. However, overcoming it provides the Werewolf with permanent Willpower.
If done correctly a GM can even get a player to do this. It's immensely satisfing when it happens.
An occupational hazard of Astartes and Guard officers in Warhammer 40,000. One of the more typical comes from the Primarch Corax: after resorting to desperate measures to rebuild his devastated Raven Guard during the Horus Heresy, he reluctantly and personally executes the horrific monstrosities his orders created, then locks himself in his room for a year and a day, after which he emerges and takes a ship on course for the Eye of Terror, his only word being "Nevermore..."
Hlaine 'Mad' Larkin, the unhinged sniper from the Gaunt's Ghosts series, has one of these during basically every battle.
While were talking about Dawn of War, I would like to take you back to the First game's Single player campaign, after grinding through Orks, Eldar and Chaos troops, Brother Captain discovers his Long Time buddy and Company Librarian turn to Chaos, though the mission's scene doesn't show exactly how long his BSOD lasted, but it was hinted that he got real mad and by the beginning of the next mission his anger was made manifest by a orbiting Battle Barge.
In the Dark Heresy expansion: Ascension an event specifically designed to cause a Heroic BSOD is one of the ways a character can be promoted to the rank of Inquisitor.
In the free Matrix game "There Is No Spoon," the Sick At Heart optional rules model damage to a character's belief system, and reduces their Matrix stat (the stat that gives them their ability to kick serious ass) on a failed Matrix roll when they choose (or are forced) to act in a way that contravenes or works to destroy their beliefs, personal code or deep abiding reason to live, or are severely tortured or have something else extreme happen to them. A character can actually be worn down to no Matrix stat at all this way, making them little more than another mook under the system's rules, and recovery of Matrix points is difficult, as it involves rebuilding the character's faith in themselves. The notes on this particular optional rule says that it should not be used excessively, as this is meant to be an action game, not a dark tale of the fragility of the mind.
Exalted has a defined set of these as part of the Great Curse afflicting all Solar Exalted. Called "Limit Breaks" (unrelated to the trope except by name), they occur whenever Exalts reach a particular threshold of stress related to their Compassion, Conviction, Temperance, or Valor traits. Effects include catatonia, Unstoppable Rage, wallowing in vice, collapsing in a fit of crying, and plenty more; all are highly destructive, incapacitating, or both. The other Exalted types where afflicted with the Great Curse has well, but it usually doesn't take this form. Sidereals, for example, run a bigger risk of everything going to hell if more then a few work together on something. (Unless you're a Lunar, where you get similar issues to the Solars, plus the ability to turn into a 2 ton killing machine at will.)
The Unconquered Sun went into one shortly before the Usurpation, and has pretty much withdrawn for 2000 years as a result. Let's put it this way: in his stronghold at the heart of the Daystar, there's a courtroom. In that courtroom, there is a list of people found guilty by the judgment of the Unconquered Sun. The last name listed is his own.
The table of possible results for a failed "Fright Check" in GURPS include a number of blue screen-style effects, of varying severity and duration. In addition, all sorts of spells, powers, surprise effects, etc., can produce "mental stun", which is essentially a very short-term BSOD.