Older Than Feudalism. After Patroclus' death in The Iliad, Achilles cuts a bloody path through the Trojan forces and doesn't stop for a couple more books. It's implied he was able to do this before, but now he's really mad. Actually, the whole epic is dedicated to 'menin', wrath. The opening line and invocation is:
"Sing goddess, of the wrath of Peleus' son, Achilles, that destructive wrath which brought countless woes upon the Achaeans, and sent forth to Hades many valiant souls of heroes..."
An Italian adaptment of the Chanson de Roland has the eponymous character gets into this state when he finds out the girl he saved and protected has eloped with an enemy soldier. The next books are all about him ravaging all around, from tearing apart any living thing he encounters to defeating an army of mercenaries throwing boulders and trees at them. To get him back to normal, his allies have to literally get his sanity back from where it fled to (the Moon).
Honor Harrington goes on several during the course of the novels, usually when someone she cares about is set upon by goons. Additionally, the entire Grayson Navy goes on one when Haven attacks Basilisk station again, as they believe that their most beloved Steadholder has been murdered by the Peeps. "Admiral Yanakov to all Grayson units," it said, and White Haven could almost hear the clangor of clashing swords in its depths. "The order is—Lady Harrington, and no mercy!"note This inspired a massive Oh, Crap on the part of Admiral White Haven, who was sure he was about to witness a massive war crime until he realised that the order was "no mercy" as opposed to "no quarter." (The former means that the victors won't be picking up survivors. The latter means that the victors won't be allowing any.)
In Mission of Honor this is what Mike Henke has Baroness Medusa and her staff do to Admiral Crandall.
Commander Vimes in the Discworld novels has occasional moments of unstoppable rage, most notable when fighting the dwarfs in Thud!, where "the Beast" that takes over at such moments is augmented by an evil psychic force. Being Samuel Vimes of the Night Watch, his sheer inner stubbornness to be a good guy and not let chaos and lawlessness win has created an inner Watchman in his psyche, to keep the Beast in check.
"You misunderstand me. I am not here to keep the darkness out. I am here to keep it in." Yeah. He fought unstoppable rage—not 'someone under rage', the rage itself as it tried to use him—and stopped it.
The rogue drow fighter/ranger Drizzt do'Urden from Salvatore's Forgotten Realms D&D novels is prone to falling into berserk rages when his self-defense reflex is triggered. Drizzt dubbed this mental state "the Hunter", as he becomes a merciless and calculating killing machine and virtually unstoppable.
In Wizards First Rule, the first book of the Sword of Truth series, when Kahlan is told Richard has died, which he hasn't, she goes into a "blood rage", killing the men who had her held down against the ground and ready to be raped without breaking a sweat.
She doesn't just kill them...
The badgers in the Redwall series are prone to a "bloodwrath," in which they become unstoppable berserkers who are blind to all but their target.
Occasionally, other creatures will go into a similar state as well, particularly Redwall Warriors if their loved ones are threatened.
The entire Hradani race of the Bahzell series. The race was originally more Elf like, being taller and having fox like characteristics along with a longer life than humans (at a cost at not being able to use magic as direct as humans). Then Wizards start experimenting with the Rage a few had. During the last war they were converted into an evil force of berserkers. Until the few with natural unstoppable rage were able to rebel. It's to the point that if you give yourself to the rage you're immune to nearly all magic. The main character nearly kills the only good wizard left on the planet when he hears the word "wizard," triggering his rage.
Hradani didn't start with the Rage - it was forced into their species by dark wizards serving the evil pantheon of that world. Even twelve hundred years later, you wouldn't want to face one of them - Hradani come in two sizes: large and ginormous. Bahzel falls in the ginormous category himself - he's nearly eight feet tall, weighs nearly four hundred fifty pounds, and he moves like a cat. And that's when he isn't using the Rage.
Deepgate Codex: Carnival is dangerous enough at the best of times, but when she gets sick of something she goes into god mode, at which point not even the laws of physics can stop her single-handedly slaughtering half an army using a regular everyday handheld gardening fork.
Harry Dresden tends to cause a lot of property damage when he's pissed off, and has, at various points: killed an enormously more powerful wizard, Justin DuMorne; redirected a lightning bolt at a demon that was chasing him; thrown a werewolf all the way through two buildings; burned down a building containing hundreds of vampires because they grabbed his girlfriend; brought out all the ghosts under the building at once, collapsing it; killed several incredibly powerful demon-possessed psychos; shredded a mob of vampires with an antipersonnel mine; blasted a huge torrent of fire straight into the middle of the Winter Court of the Sidhe... Well, you get the idea.
And all that pales in comparison to "Blackstaff" McCoy, who in a fit of rage over a threat to someone he cares about yanks a old Soviet satellite out of orbit and drops it on a vampire nobleman's estate just to make a point. Or later, when defending his family and friends simply rips the life out of dozens of people. No fire, no explosions, he just points at them and they die.
A particularly extreme example of this is Icarium from Steven Erickson's Malazan Book of the Fallen. Icarium, normally a gentle and creative fellow verging on pacifism, has a tendency to go into a berserker mode that's downright genocidal when provoked, usually followed by an inability to remember what just happened. In milder cases, this means he wakes up confused among the gutted bodies of whatever ferocious pack of creatures just attacked him. In a few more extreme cases, he woke up among the shattered ruins and dead citizens of entire civilizations, completely unaware of what had just transpired.
In The Pendragon Adventure, Saint Dane has a habit of confronting Bobby in order to smack him around for the hell of it. For the most part, though, he's just egging Bobby on as part of his Mind Screw technique. This changes in Rivers of Zadaa when Bobby - in the midst of being smacked around - stands up to Saint Dane and claims that the villain is getting desperate because he is losing the overall war. Saint Dane utterly snaps and proceeds to beat the living shit out of Bobby, to the point where Bobby spends a month in a hospital before he can walk again.
Each of the villains in the series represents a deadly sin, with Sir Thursday representing wrath. He beats his subordinates for minor failures and deeply enjoys battle. At one point he kills children who have been enchanted into motionlessness just because they are not obeying his orders. They're not "following orders" BECAUSE THEY CAN'T MOVE. Thursday doesn't care.
The part of the Will he guards, which symbolizes Justice, has anger issues as well, spitting in the face of someone during a parley.
Darkest Powers: Although Derek keeps his cool when he's the one in danger of being seriously hurt, possibly tortured, or killed, the same does not hold true when other people are at risk. Being a werewolf, Derek's rational mind will shut down and give way to pure "protect my pack" instinct when the tiny number of people he actually cares about are in danger. At least one person is already spending the rest of his life regretting having threatened Derek's brother.
Mrs. Weasley shows a bit of this in Harry Potter and the Deathly Hallows with her famous line "NOT MY DAUGHTER YOU BITCH!" followed by the death of a certain loyal female Death Eater. That proves never to mess with one of Mrs. Weasley's children. (This includes Harry, who earlier in the series she outright declared was her own son in all but blood.)
Hagrid may be a Gentle Giant, but if you do manage to get him into a real temper you'll find out that he's partially immune to spell damage and has more than enough strength to take down five armed attackers with his bare hands.
Harry himself shows traits of this. Despite being a fairly decent person, he too has moments where he looses control of his temper. One good example would be after Bellatrix murders Sirius, where Harry briefly uses the Cruciatus curse to bring her down.
But the horror that paralyzed and destroyed Ascalante roused in the Cimmerian a frenzied fury akin to madness.
Touchstone in the Old Kingdom series. In the first book, Sabriel is shot with an arrow and he runs very, very fast. Later a Noodle Incident is mentioned in which a fake ambassador (a 2 metres tall barbarian) tries to kill Sabriel with a toasting fork; Touchstone grabs him and throws him down the table while roaring with rage. He then tries to throw the throne after him.
In the Lonely Werewolf Girl books, Kalix's unstoppable rage when she goes wolf has been the downfall of more than one werewolf hunter.
This trope is an inherited characteristic of the Viking-descended Barnikel lineage in Edward Rutherfurd's multi-generation historical novels. Do not anger a member of this family, whether it's by threatening to expose their role in La Résistance or abusing a puppy in front of a fifteen-year-old Barnikel boy.
Visser Three in Animorphs had one of these several times a book practically.
In one novel, Unity, protagonist Andorian Shar enters a state of Unstoppable Rage when battling a Kurlan-possessed woman aboard Deep Space Nine.
In an earlier book, Twilight, he enters one while incapacitated by injury and so takes it out on the ground by slamming his fist against it repeatedly (causing himself further injury).
In The Lord of the Rings Éomer holds himself together rather well when his uncle, King Théoden, is slain in the Battle of the Pelennor Fields, but when he unexpectedly learns that his sister Éowyn died (or so he believes) too, he quite loses it. His troops take heed:
"Then without taking counsel or waiting for the approach of the men of the City, he spurred headlong back to the front of the great host, and blew a horn, and cried aloud for the onset. Over the field rang his clear voice calling: 'Death! Ride, ride to ruin and the world's ending!' And with that the host began to move. But the Rohirrim sang no more. Death they cried with one voice loud and terrible, and gathering speed like a great tide their battle swept about their fallen king and passed, roaring away southwards."
Also the Ents, considering how docile they are and how long they generally take to deliberate upon matters. Saruman's treachery invokes such a fury in them that Isengard and all its orcs could do nothing to stop the raging ents.
In The Silmarillion, we have several characters succumbing to Unstoppable Rage, most notably Fëanor and Túrin.