Super-strong, invulnerable and out-of-control. Flee.
The Incredible Hulk in every incarnation and medium, as his strength is fueled by rage.
In Marvel's World War Hulk storyline, he's busy with a particularly Unstoppable Rage, mopping the floor with everyone in his way. The truly frightening thing was that he had gone into Tranquil Fury at the same time, leaving him with enough mind to keep his head and employ strategy and trickery.
Beneath her calmer exterior, Betty is nearly as repressed as her husband. When she turns into Red She-Hulk all that rage finally gets an outlet.
This is also one of Wolverine's defining traits. He's usually composed and calculating when he fights, but when he's pushed beyond a breaking point, he gives in to his animal instincts and his fighting style becomes more erratic and feral, and it's usually in these occasions where his body count rises the most.
Like father, like daughter. Do not attempt to hurt Wolverine or anyone else X-23 loves, or you'll be sent home in pieces. She's also seen blowing her top when confronted by former members of her dead former pimp's gang, who were continuing to traffic women. Being under the effects of the Trigger Scent takes this Up to Eleven, and she becomes a virtually unstoppable whirling ball of adamantium-bladed death that will tear apart everything in her path. In this state she's completely unable to distinguish friend from foe until it wears off, and yes, it has been used to make her hurt people she cares about.
Laura: The ones who made me, they made a chemical...a scent...when I smell it, everything goes black and when I wake up, everyone's dead.
If Hulk weren't the poster boy for this trope, the Red Lantern Corps in Green Lantern would be. Their rings are powered by their rage, which is strong enough to the point where all but their leader are mindless berserkers.
In the Hush storyline, Batman goes into one of these when it seems that The Joker killed his childhood friends. Flashing back through all the people the Joker's victimized and killed over the years (mostly Barbara Gordon, Jason Todd, and Sarah Essen), he goes into an Unstoppable Rage, taking down Harley Quinn and Catwoman (the latter of which was on his side, but simply trying to stop him from killing the Joker), and stalking the Joker through an alley. It takes Jim Gordon to snap him out of it, and, even then, Gordon had to shoot him to get his attention. Even after getting shot, Batman's still thinking of all the different ways he could kill Joker (something along the lines of "pushing his skeletonthrough his mouth"), but at least he wasn't choking him any more.
In Superman/Batman #1, Batman finds himself witnessing a similar situation between Superman and Lex Luthor. He notes the similarities between this and what happened in Hush, and then, instead of talking him down like Jim Gordon did (he even notes that he wouldn't do that), he notes to Superman that he could make Luthor's death look like an accident, and then he gets Superman to stop by directing his attention to something else that needs to be done that's more important.
In the film adaptation, Superman/Batman: Public Enemies, Supes goes even further when Batman, instead of Captain Atom as was the case in the comics, attempts a Heroic Sacrifice by manually piloting Toyman's rocket to destroy the asteroid. He then gives Luthor the beatdown of his life and only stops fuming when he learns there's a chance Batman is still alive.
Superman: That was my best friend... and you just killed him!
Similarly, Nightwing flies off the handle and kills Joker (Batman revived him, mostly because his proteges have no business becoming murderers) when he believes Joker has killed Robin III and Joker has also taunted him about killing Robin II (Jason Todd).
Joker: I hit Jason a lot harder than that. His name was Jason, right?
Another example happened during the "Back In Black" story arc following Civil War. Aunt May lay dying after taking a sniper's bullet meant for Spider-Man. Donning his black costume, Spider-Man tracked down the man responsible, The Kingpin (who was serving prison time at that point), broke into the prison, confronted The Kingpin and then proceeded to give him a very savage beatdown. No jokes, No quips. He ends it by threatening to fill Kingpin's throat with enough webbing to kill him if he ever threatens Spidey's loved ones again.
Krypton No More: After finding out that the Kandorians talked his cousin into lying to him, Superman is so furious he flies off to fight an invading alien army because he aches to punch something.
In The Supergirl from Krypton, Darkseid tries to kill Supergirl and believes he has succeeded. The mere sight of Supergirl's seeming death makes Superman go ape-shit over losing her and beats Darkseid to a pulp.
Supergirl: Kara is - usually - a very nice, kind person, but she's also a Hot-Blooded, short-tempered teenager who protects her loved ones fiercely, and she has occasionally gone on a rampage:
In the Crisis on Infinite Earths, when the Anti-Monitor threatened with killing her cousin Superman, she went berserker and almost killed him. Yes, she nearly killed a being that devours universes.
Also, Matrix during her mini-series back in The '90s discovered that her lover Lex Luthor had made thousands of clones of her from the residue he collected after her fight with Doomsday. She was very close to killing him too.
The trope is called out by a patron in a diner who sees it on the news: "That guy is gonna go fuckin' berserk..."
Mayor: And the good news? Johnathan: Crime's down.
It was so bad that he wasn't even really aware of what he was doing each time until the recoil from his gun kicked in. He was in a sort of perpetual hallucination until his family was returned to their grave.
The final arc from the Star Fox comic run in Nintendo Power had Fox McCloud going berserk upon learning that Andross was responsible both for his mother's death (a car-bomb meant for his father) and his father's disappearance in the Black Hole (because Andross sabotaged his ship). He proceeds to sport Glowing Eyes of Doom and tear the bad guys apart before going after Andross in person, but in a rare moment of not getting in the last shot like he usually does in battles, he allows Andross to escape into the Black Hole because he knows his father is going to find him and "he deserves the last shot after all these years."
Scrooge McDuck has many famous comic book iterations of this, but none quite as amazingly awesome as in the "Yukon Scrooge" storyline. The bad guys capture Scrooge to steal his land claim and gold. They then torment him by reading his private mail and taunting him with the death of his mother. A 45 Kg Duck proceeds to throw a concert piano out the window and destroy a riverboat with his bare hands.
Another great one (though nowhere near the havoc he caused in Yukon) is in the story "The Terror of the Transvaal", when Scrooge helped out Flintheart Glomgold (a future nemesis of Scrooge, with this event triggering their rivalry and hatred), who had been tied to a buffalo for stealing diamonds from a mine and the buffalo sent to the savannah, with Scrooge unaware of the theft. Then during the night Flintheart robbed Scrooge and snuck back into town. When Scrooge woke up and realized what had happened, he got angry enough to tame a lion by yelling at it, after the lion had roared at him. He then rode back into town with the lion.
Tycho Celchu in the X-Wing Series, at least in the comics - in the novels, Isard apparently managed to neatly excise his ability to be angry - gets mad◊ and starts swinging◊ very easily.
Gentle Giant Hulkling of the Young Avengers falls into this when his boyfriend Wiccan is erased from reality. The only reason he didn't attack/possibly kill Iron Lad is because Hulkling disappeared next.
Speaking of Wiccan, for the love of all that is good do not threaten his boyfriend. The last time this caused a temper tantrum, he made the Avengers and X-Men worry about a repeat of his mother. When Warden tried cutting up Hulkling, Wiccan would've killed the man if he could.
Colossus, normally the Gentle Giant of X-Men, is also one of the last people you ever want to get mad. Just ask Riptide. Just ask Ord from Joss Whedon's Astonishing X-Men run! Imprisoning and torturing him for two years to create a "mutant cure?" Very bad idea.
Ord: "It matters not that you escaped. Do you think that because you are made of mere metal that you can stand against me?"
Colossus: "I am not made of steel. Rage! I am made of RAGE!"
Wulf in Strontium Dog, being a Viking, becomes a literal berserker when he gets really mad. In this state, he's capable of beating up even Johnny.
Raghnarok, a French comic about a young dragon, features this. When Raghnarok (the young dragon) disappears, and his mother can't find him, she gets increasingly violent as time goes by and her eyes turn red. Over time, her purple scales turn black and she goes from being perhaps 12 feet tall to dwarfing skyscrapers. She then goes on to violently wreck everything in her way while shouting her son's name. This goes on uninterrupted for ten years, and she has the entire world fearing her. All armies run at sight. Her anger is only quelled once she meets her son again - and it's notable that she is a lot smaller after stopping her rampage.
In Archie Comics' Sonic the Hedgehog , the eponymous character suffers this at times despite his calm and carefree nature, particularly when his family and friends are in danger.
In the "EndGame" arc (issues #47-#50) when Knothole Village was seemingly destroyed by Robotnik's doomsday weapon (but in the end learns that it was trapped in another timezone for a short time).
Likewise in the same arc, a character named Hershey the Cat pummeled her ex-boyfriend Drago Wolf to a pulp after learning that he tricked her into killing Princess Sally (the princess herself survived, however).
Knothole was recently destroyed (for real, this time) by Eggman's air fleet, angering Sonic. It wasn't until he was taunted about the limit of his abilities when Sonic snapped and launched a devastating, but failed, Sonic Boom attack on Eggman's most powerful robot.
To paint a better picture, after the taunt mentioned above, Sonic ran off and in a few seconds was on the other side of the continent before turning around and making a beeline toward Eggman's robot. It was one of the more impressive things Sonic has done, short of being Super Sonic.
Tails, at one point, fought Sonic because he was tired of being treated as a little kid, but mainly because Sonic at one time had dated his friend's love interest, Fiona Fox. Tails was heartbroken that Fiona never loved him because of age difference, and instead loved Sonic. He was even more devastated because she was really in love with Sonic's evil twin, Scourge. He eventually went all out on Sonic while trying to rescue his dad. After Sonic learned that his friend's rage came from that fact that he took Fiona away from him, he apologized and explained his actions, and they soon made up.
Mighty is also prone to these when something bad happens to Ray the Flying Squirrel. The results are never pretty.
The Hard Goodbye from the Sin City series features Marv going on one for about a week straight, eventually taking on one of the most powerful crime families in the country. This was all because they killed one of the few people that was nice to him.
For Wonder Woman and other Amazons in their pre-Crisis incarnations, the Bracelets of Submission acted as a check against the use of unrestrained power. If Wonder Woman's bracelets were removed, she became intoxicated with power, violent and nearly unstoppable.
In Runaways, during the "Home Schooling" arc, a missile strikes the team's Malibu house, killing Old Lace and injuring Klara. Upon regaining consciousness, Klara freaks out and causes a forest of vines to grow and consume the house.
Similar to the Wonder Woman example above, Orion from the New Gods has an intense, building rage inside him that's held back by a Mother Box. The reason for this is that his father is Darkseid, and the burning hatred for all living things is In the Blood.
The Marvel Killer Robot called The Fury was a nigh unstoppable juggernaut created by an insane Reality Warper for the sole purpose of killing superbeings. It was so good at it that it eventually killed his own creator (or at least an alternate universe version of him who was just as powerful). But in the end, it was ultimately brought down by Captain UK. For much of the story, she was paralyzed by guilt and grief since the Fury killed everyone she ever knew and loved with her powerless to stop it. When she saw the Fury about to kill Captain Britain, something in her snapped, and she tore the Fury apart with her own hands, while crying, cursing, and howling with rage. In its dying moments, the Fury knew fear, pain, death and defeat.
In the Secret Wars (2015) tie-in Planet HulkSteve Rogers is on a mission to rescue Bucky from the Red King, a Hulk, who is keeping him prisoner. After a long journey Steve finally makes it to the Red King's throne room only to learn the Red King killed Bucky a long time ago. This enrages Steve to the point where he simply starts whaling on the Red King with his shield — who tries but doesn't get in as much as a single punch — and doesn't stop bashing in the king's head until he is dead. Steve literally beat the king of the Hulks to death with nothing but his shield.
A super-villainous example is DC's Doomsday, a genetically-engineered weapon created on Krypton before it was destroyed who first appeared in The Death of Superman. Through a torturous process of sending the infant Doomsday to the Death World regions of the planet and then creating a fresh clone from the remains when it was inevitably killed, it was eventually given super-human powers of survival, including a Healing Factor and Adaptive Ability... and also driven completely insane. Doomsday's mind is nothing but a morass of rage, hatred and terror; possessing the genetic memory of untold painful deaths, it lashes out blindly at all life it encounters, as it has fixated on the idea that other lifeforms are the enemy. All life.