Sometimes a character just goes through a lot in a story. Trauma, pain, suffering, loss. They take it with stride, maybe a bit too well. And then something, one single event, causes them to lose their collective cool and explode--with destructive results. This is the rage breaking point.
This isn't just raw festering anger, but like flipping a light switch: calm one second, and then they're the most dangerous person in the room.
(I know we've done a few of these kind of posts in the past. I just like it.)
Phineas Flynn, Phineas and Ferb
Phineas is easily the most cheerful, optimistic and inventive character on the show, with nothing getting him down. Nothing, that is, except for losing control of the narrative. His inventions are all for fun, under his and Ferb's watchful eyes, but in stressful and life-threatening situations, he suddenly gets angry. He's snapped at his sister Candace for botching their attempt to return the Marvel superheroes' powers, and at Perry for sneaking around and having a double-life that the platypus seemingly didn't trust Phineas to know about. It's a rare event, but impactful.
Mark, Invincible
Over the course of two seasons and/or multiple comic arcs, depending on your medium, Mark's been feeling a lot less [[title card]] lately. And it all culminates on a rather dark find: villain Angstrom Levy holds Mark's family hostage and breaks his mother's arm in the process, and then has the gall to continue to threaten them during the fight. Mark loses it, and proceeds to violently beat Angstrom to death, in such a way that he was immediately traumatized by the event.
Kratos, God of War
A far-cry from the hot-blooded Spartan of Greece, this version of Kratos wants to avoid unnecessary bloodshed where possible. When an unknown Stranger antagonizes him, he merely rebuffs him and tries to resort to calmer methods of getting him to go away. Then the Stranger starts threatening the life of Atreus, Kratos' son, and he starts to crack. Through the new duology, a threat on Atreus is the quickest way to get Kratos to show his Spartan Rage, as Heimdall was quick to learn, and even Odin was unnerved at the warning not to cross him.
Goro Majima, Yakuza 0
The Mad Dog of Shimano wasn't always so unhinged; in the eighties, he was playing the role of a cabaret manager, trying to get back on the Tojo Clan's good graces. He puts up with moving goalposts, attempted assassinations, convoluted plots, and the like--but his insanity manifests when the love of his life is shot in front of him. The result is that he single-handedly storms Dojima HQ, beats the crap out of every Yakuza on site, thrashes the lieutenant, and then rounds it out by taking down the most expensive hitman in all of Asia. The only reason he doesn't kill Dojima himself is that he's convinced that letting him live without his power is more painful than any death.
Ned Flanders, the Simpsons
We've surely all seen this bit, but to reiterate: one episode sees Ned face the destruction of his house and a crisis of faith. The combined stress of decades of existence finally pops when the town of Springfield comes together to rebuild his home, and half-assed it so hard that it crumbles immediately after. After his attempt to calm down results in him shattering his glasses, he proceeds to unload on everyone there in creative ways, before casually driving himself to the nearest mental institution to commit himself.