In Lock, Stock & Two Smoking Barrels, Big Chris, for all his ruthless coercion and threatening demeanor, is rather a reasonable chap . . . until a man takes his son prisoner. He goes full Papa Wolf on the man, smashing his head repeatedly in a car door while roaring incoherently.
Luke Skywalker spends most of the original trilogy actively not giving into anger, because that leads to The Dark Side, but when Darth Vader makes the mistake of threatening to turn Leia to the Dark Side during their final confrontation in Return of the Jedi, he immediately goes berserk, interrupts Vader's sentence, and beats Vader on sheer, Force-augmented aggression (despite being a full foot shorter and with the corresponding reach disadvantage), only stopping after he chops off Vader's mechanical hand and realizes just how close he just came to becoming like him.
It runs in the family: when Anakin completely destroys a village of Sand People after they killed his mother. "Not just the men, but the women and the children too."
The final Luke-Vader duel would be the Ur Example of sometimes-Force-enhanced psychological warfare gone wrong. Although, sometimes spurring someone into this (particularly with repressed anger) was actually the intended effect; Palpatine had actually been attempting this on Luke right before and after the duel... but his obviousness of intent probably helped Luke pull himself back from the brink.
It could be argued that provoking Luke to that level of rage was exactly Vader's intent.
Obi-Wan Kenobi after Darth Maul mortally wounds Qui-Gon Jinn.
Subversion: In Mystery Men, Ben Stiller's character Mr. Furious was a superhero seemingly built around Unstoppable Rage - except that when he raged, he wasn't much less stoppable than a "normal" adrenaline-fueled angry person. He didn't become substantially stronger, tougher or faster, which wasn't very useful. During the final battle, however, his rage apparently gave him enough momentum to overcome the Big Bad. In fact, it is implied that his "rage" had really been an act until that point.
Oddly enough, in both Good Fellas and Casino, Joe Pesci seems to have a dangerously psychotic Unstoppable Rage that goes off from something as simple as a misunderstood compliment. Actually averted in Pesci's famous "You think I'm funny?" scene. He's just screwing around with Henry Hill. What he does to Billy Batts and Spider, on the other hand...
Go ahead. Fuck with Godzilla's kid. That's a dare. That's a double-dare. No matter what the timeline, fucking with Godzilla's kid is a very painful way to commit suicide, because Godzilla won't just KILL you, he'll END you.
In 300, the Captain flies into such a rage when he sees his son Astinos get his head chopped off on the battlefield during a lull in the action. A decent amount of single-handed ass-kicking ensues, until three of his fellow Spartans have to physically restrain him and drag him back to their camp. This is even more Bad Ass when his screams are carried all the way to the Persian camp, and scares them more than the deepest battledrums.
The 3rd act of the Jackie Chan film Police Story features a rare look at Jackie's typical happy go lucky character snapping and going to town on everyone that's done him wrong. This includes beating the crap out of people who can't fight worth a damn like a doctor and a lawyer, but they've all been such huge jerks through the whole film that it's easy to cheer him on every step of the way.
In The Patriot, French & Indian War veteran Benjamin Martin is fueled with unstoppable rage when his second-oldest son is shot point blank by the evil British Cavalry officer Col. Tavington. With minimal help from his two pint-sized sons, Ben brutally takes down a contingent of British Redcoats, not satisfied with making them dead but burning through all of that rage by hacking at one soldier's bloody corpse.
In Legends Of The Fall, Brad Pitt's character Tristan Ludlow goes on an Unstoppable Rage-fueled Roaring Rampage of Revenge after he watches his younger brother die on a WWI battlefield from machine gun fire and mustard gas. He not only slaughters every German in the vicinity but arrives back at field camp the next morning wearing warpaint of mud and blood and strings of fresh German scalps.
In Transformers: Revenge of The Fallen, Optimus Prime fights Megatron, Starscream and Grindor by himself and is eventually overpowered and blasted halfway across a forest area. After Megatron tries to justify his means for wanting to kill Sam, Optimus denies his reasoning, charges right into the midst of them, slices off Grindor's arm, beats down Megatron, slices off Starscream's arm (and whacks him across the face with it) then leaps onto Grindor and tears his face in two, killing him.
"You'll never stop at one! I'LL TAKE YOU ALL ON!"
In DOTM, Optimus might as well be fueled by Unstoppable Rage.
"We will kill them all"
The eponymous hero in the Spider-Man Trilogy flies into a fit of rage anytime his loved ones are threatened or harmed, usually resulting in beatdown for the villains.
In Spider-Man, Green Goblin taunts that after finishing him in their fight, he will kill Mary Jane, whilst making her death 'nice and slow'; Spider-Man quickly recovers and beats the crap out of him.
After kidnapping Mary Jane in Spider-Man 2, Dr. Octopus rather smugly refuses to give up her location and Spidey attacks him in retaliation.
This happens several times in Spider-Man 3, once where he confronts and almost kills the Sandman for killing his uncle, the next where he thrashes Harry Osborn in his own home for ruining his life with Mary Jane, the next where Harry takes a blow (two spikes attached to his board) from Venom meant for Peter and is killed because of it.
Ralphie in A Christmas Story. After getting a C+ on his "What I Want For Christmas" essay, and feeling really despondent, neighborhood bully Scot Farkus pelts him in the face with a snowball. After he adds some verbal taunting, Ralphie snaps and beats the everloving crap out of him, while other neighborhood kids look on, reducing Farkus to a sobbing, miserable wreck.
Kham in Tom Yum Goong (aka The Protector). After discovering that his elephant had been butchered and the bones set with gold and jewels, he goes into serious Heroic BSOD mode. He doesn't notice the horde of thugs beating on him until one makes the mistake of stabbing him in the side. This snaps him out of his grief and turns his BSOD into a Roaring Rampage of Revenge.
The Fugitive: Richard Kimble displays this upon finally encountering the man who murdered his wife, and upon confronting his so-called friend who set the murder plot in motion.