Normally in a game of Warhammer 40,000, casualties cause squads to have to pass a Morale test or fall back. Space Marines of the Black Templars chapter, however, are so fanatical that the sight of dead comrades makes them charge forward to avenge the fallen. This occasionally leads to a squad's Sole Survivor assaulting a daemonic manifestation of blood and rage.
The Blood Angels chapter has a different problem, brought about by the Genetic Memory of their Primarch's death during the Horus Heresy. Battle-brothers are sometimes afflicted by the Red Thirst, driving even heavy weapon troopers to abandon their positions and try to tear apart the foe in close combat. A worse case is called the Black Rage, whereupon the eve of battle, a Blood Angel completely forgets his own identity as he hallucinates his Primarch's final moments. Such unfortunates are placed in the Death Company to form berserker assault squads, and any survivors are granted the Emperor's Peace after the battle.
Khorne Berzerkers, obviously, are so full of bloodlust that they Feel No Pain and barely remember to fire their pistols in their haste to maim and kill with their Chain-Axes. Kharn the Betrayer is legendary for being so consumed by rage that he never misses in close combat - he either hits the enemy, or someone on his own side. In fact, he'll happily take the skulls of his supposed allies for want of another foe to kill.
Amusingly, there was a Chaos battleship named the Unstoppable Rage, but it was destroyed by an Eldar vessel and so didn't really live up to its moniker.
One of the special abilities of the Tau Ethereal leader Aun'Va is that he is so beloved by his troops that if he dies, he triggers an Unstoppable Rage in all Tau troops in line of sight, giving close combat bonuses to an army that normally prefers to blast apart foes with Beam Spam.
Eldar, being psychic race, weaponized emotions. As a result, their more offensive aspect warriors and warlocks (technically, also an aspect warrior that walks path of Seer) develop split personality that is nothing, but a swirling ball of hate. Exarchs are aspect warriors that can't turn this personality off.
The World of Darkness gamelines feature this trope, mainly with the vampire and werewolf games in both systems.
When a vampire character in Vampire: The Requiem or Vampire: The Masquerade enters a Frenzy and lets the Beast within take control, he or she can tear lesser foes to shreds and overwhelm another vampire, as they are able to ignore all wound penalties. A more powerful (and usually elder) vampire can still take a frenzied vampire down, especially if he goes into frenzy himself. Vampires interested in maintaining the Masquerade frown on those who frenzy, while those who aren't tend to embrace it.
Werewolves from Werewolf: The Forsaken and Werewolf: The Apocalypse have the Frenzy ability as well, and alternately embrace it and fight it (noted that vampires, in game terms, roll to resist going berserk; werewolves roll to both resist and trigger it). They tend to have an even easier time than vampires, since frenzy is always accompanied by turning into a 9 foot-tall lupine death machine... that paradoxically makes their Masqueradeeasier to maintain due to something called the Delirium. Still, Forsaken calls it "Death Rage" for a good reason.
In Werewolf: The Apocalypse, going too deep into Frenzy causes the werewolf to enter "Thrall of the Wyrm" in which they go absolutely bonkers. This results in either shredding everything in sight, eating everybody in sight, or violent necrophilia, and always a ton of shame when the perpetrator regains their wits. There are also a few Gifts, such as the wereleopard Gift Shiva's Might, that lets the character deliberately enter a (normal) Frenzy.
Both gamelines' vampires and werewolves can instead enter Unstoppable Terror — known as "Rötschreck" for vampires (either line) or "fox frenzy" for oWoD werewolves — with the victim fleeing in blind panic from the trigger, tossing aside or shredding anything that stands in the way of doing so. In New World of Darkness and Werewolf: The Apocalypse it's treated as another facet of the Unstoppable Rage, while Vampire: The Masquerade treats it as an unrelated phenomenon also originating with the vampire's Beast. In Werewolf: the Apocalypse, shapeshifters experiencing this will normally take their full animal form for speed — Forsaken's werewolves become the 9-foot tall lupine death machine for either type. Werewolf: The Apocalypse has human witnesses freak out any time they see a werewolf or other shapeshifter in their hybrid form.
Prometheans also have their own state of emotional disarray, known as Torment. How rage-filled Torment really is depends on the element of the Promethean's humor, but each one has some elements of Unstoppable Rage. Frankensteins (fire) and Tammuz (earth) have the more traditional "Hulk Smash!" rages, Galateids (air) tend to go all Fatal Attraction when it comes to obsessing with others, Osrians (water) go cold and emotionless, and Ulgans (spirit) lock onto whatever spirit is closest and copy its traits. And then you've got the rare nuclear Prometheans, the Zeka, whose Torment tends towards "destroy everything." And, for added fun, instead of prompting normal Disquiet in vampires and werewolves, Prometheans instead cause an unsettling feeling in them that makes it increasingly more difficult for the other supernatural to resist Frenzy or Death Rage the longer they stay together.
Sirens from the fan-made supplement Siren: The Drowning can suffer their own variant of this trope, Maelstrom, whenever their standards for Civilization and/or Nature are violated in their presence or when something or someone they deeply care about is harmed. This usually causes them to lash out at whatever caused this harm and stay in that state until the responsible either leaves their reach or dies. Like vampires, this allows them to ignore wound penalties, but also to use their Alterations and Verses faster.
In Dungeons & Dragons, a base class, the Barbarian, is built around this idea. Rage is the Barbarian's primary special ability, allowing them a marked increase in their physical prowess and mental fortitude in exchange for a slight decrease in their willingness to dodge blows and think straight. The ability becomes more potent as the character's level rises. Unlike most fictional versions of this trope, Barbarians may invoke and end their Rage at will (but are limited to one rage per encounter), not in response to any specific trigger.
Third Edition also has an "on steroids" — or perhaps, "on 'roid rage" — prestige class version of the barbarian: the Frenzied Berserker. The main difference is that there are few defensive benefits to a frenzy (but see below) as opposed to a rage, that its bonuses and penalties can stack with a rage, that frenzy will continue until its time limit expires or the character forces himself out (rage can be ended at will, but you need to make a Will save to end a frenzy) — and if he runs out of enemies the character will attack anyone in the vicinity, including allies — and finally that it can be triggered by damage as well as entered at will. Finally, he can also inspire frenzy in his allies, which if you consider that most frenzied berserkers probably hang around a lot of barbarians and fighters as opposed to wizards and rogues is a very scary thought.
This is a very good example of the trope, as a properly built Frenzied Berserker is one of the most powerful physical combatants possible under 3rd and 3.5 edition rules—without even going into epic level, a half-orc Frenzied Berseker could have a Strength of 36 while in a raging frenzy. This is enough to match or out-muscle most high-level fiends and celestials, all but the oldest and mightiest dragons, and many lesser deities in terms of raw strength.
The berserker's frenzy has a tropetastic defensive benefit. While Frenzying, HP damage will not kill him until the Frenzy is over. There's also a feat which lets him delay the effect of any attack until the end of the Frenzy. This can lead to some very interesting moments if he's hit with the big bad's Wave Motion Gun during his Frenzy. Also a notable counter for many damage-output Min-Maxing builds. See Glass Cannon. Sadly, this can be stopped suddenly by a 2nd-level spell called "Calm Emotions".
Dragons have a boosted one of these in a prestige class called the Bloodscaled Fury. It's compared to a barbarian's rage as a barbarian's rage is to a child's temper tantrum.
There's also the Tainted Raver template, which is a person driven mad by the taint mechanic. Basically, they're permanently raging, but with the ability to do anything their class could normally do, like spellcasting.
And now there's Fourth Edition, which introduces the Barbarian again. The 4E Barbarian is a bit more primal than his 3E counterpart, and his Daily powers, known as Rages, give effects that last for the entire encounter or until he enters a new Rage, give his At Will powers more power, and allow him to dish out Rage Strikes that expend unused Dailies to deal more damage against an enemy.
Pathfinder allows barbarians the option of performing any number of superhuman feats, or shaking off any number of incapacitating effects, while raging.
Limit Break in this game is part Heroic B.S.O.D. and part Unstoppable Rage. After having their virtues pushed to the breaking point, many Exalted will either A) act towards them with little thought of restraint, or B) act against them with little thought of restraint. This can get messy fast when the Exalt in question values Compassion or Valor. The two Solar Limit Breaks that best exemplify this are Berserk Anger and Red Rage of Compassion. RROC is slightly less psychotic but still tends to cause collateral damage on par with a very cranky airstrike.
The Lunars can become the very embodiment of this trope using the aptly-named Endurance Charms. One charm lets you shrug all damage as long as you channel Essence to it, another lets you not drop dead even if you, by all rights, should be. The fluffs say that Lunars using those charms raged for days as the world arrayed to kill them and their Solar mates.
Solars also have a Resistance Charm that allows them to do this. Prematurely ending it takes a significant mental toll (it costs a ton of Willpower points and accumulates a lot of Limit) unless they are restrained by a friend or loved one.
And then there is an expansion to Infernal Monster style by Ink Monkeys, which puts its possessor into a permanent state of Unstoppable Rage. The name? Untamed Apocalypse Shintai.
Righteous Fury mode is the Buffy and Angel RPG version of Unstoppable Rage. A character can spend two Drama Points to go into Righteous Fury mode, but only in response to something very bad and deeply personal happening, like a brutal attack on a loved one, an unexpected and very nasty betrayal, or the raising of a monstrous former lover killed years ago. When in this mode, the character gets a + 5 to all attack actions for the rest of the fight, which is cumulative with Drama Points spent for Heroic Feats. Even a White Hat can kick serious ass when properly motivated like this.
13th Age has the Barbarian, whose berserk rage allows them to roll twice for every attack and pick the best, but there's also the Sorcerer - those who take the Infernal Heritage Talent can enter a spell-frenzy that lets them roll twice for every attack, but each die that comes up a miss will kick you in the head just a bit.
Explicitly the case in BattleTech when legendary mercenary leader Jamie Wolf was killed in battle defending their home world of Outreach due to treachery by Word of Blake backed rogue mercenaries. Upon hearing the first news of his death, the entire unit, five regiments strong, went to something called Condition Feral. Anyone not wearing a Dragoons identifier on the planet instantly became targets—allied units were given exactly one chance to stand down. Any unit that did not take the (in hindsight very generous) offer to stand down, or any unit that was not an allied force, were completely oblierated by overwhelming firepower from the best-armed mercenary unit in the galaxy. So thorough was the savage fury of the grieving, angry Dragoons that they annihilated entire enemy regiments where they found them, showing no mercy and offering no chance for surrender.