A schizophrenic will occasionally have a fit of "Hulking out"; they cannot experience pain during this fit, nor will they know what's going on around them. It's actually quite saddening, when you think about it...
Some forms of Pervasive Developmental Disorders feature this as well; it's called a "werewolf" state.
It can happen with drugs as well (such as Meth "tweaking" and PCP)
This has the unfortunate side effect of killing many users. While mostly a myth, police have had to 'put down' an assailant because they couldn't be taken without severe risk to the officers in question or civilians. It's not as common as many sources say, but it does happen. Unstoppable rage does not equal bullet proof.
'Roid rage doesn't happen as often as people believe. But some users experience severe aggression spikes. See the Lifestories: Families in Crisis "A Body to Die For: Aaron Henry" for a direct account.
What's more amazing is that he did something like this again, although the second time around was more of the Tranquil Fury variety. In a French battle about six months later, by this time Second Lieutenant, after having sent the remaining 19 of his original unit of 128 men to retreat and take cover, he jumped onto a disabled and burning tank destroyer and proceeded to use the .50 cal machine gun to hold off the approaching Germans for an hour during which time he was shot in the leg but kept going. The day before, he had also taken some shrapnel from a mortar that had killed two nearby men in his unit.
The number of unbelievable things Audie did during WWII has to be read to be believed. He had balls of adamantium-plated depleted uranium and was as close to actually being Wolverine as anyone in real life could be.
Adrenaline will make anyone faster, stronger and more likely to ignore pain and such. Such as when you put a person or animal into a life-threatening situation they can't run away from.
There is some truth to the phrase 'Strength of a Madman', our muscles have actually hardcoded to not function to full power to avoid damaging the skeleton. Madmen in fits of rage have shattered their own bones by punching that hard.
There was one famous case where a mountain climber/hiker was pinned under an enormous slab of rock. His body went into survival mode, where he pushed the slab off of him. He exerted so much pressure that his muscle was torn from the bone in his arm. For reference, the rock this moderately-built hiker pushed off of himself weighed over 700 pounds.
Marion "The Barbarian" Barber of the Dallas Cowboys and Bob Sanders of the Indianapolis Colts are two NFL players whose style has been described as such. Unfortunately, for the latter this has left to a number of serious, often season-ending injuries.
hide, late X Japan guitarist, was allegedly prone to these. One incident, mentioned by Taiji Sawada in his band autobiography, referred to hide going into a drunken rage, and fighting with hotel deskpeople....
Taiji Sawada himself, and the official story is that this is what led to his arrest (after which he subsequently died a suspicious death in custody): he had apparently gotten so angry at his manager over her stealing from him that he chose to pick a fight with her. On an airplane...which did not end well for him.
Male elephants in a state of musth become hyper-aggressive and nearly impossible to control.
Ditto for any (unneutered) male ungulate in rut, e.g. bulls.
It gets better. The one she killed was the leader of the terrorists. There was a decent reward on his head, and it was given to Rukhsana.
Léo Major in Zwolle during World War II. After his friend, Willie Arseneault, was killed by a German sniper outside a bunker, he went into a rage, killing two of the soldiers inside before the rest fled, leaving behind a munitions dump. He used the captured munitions to libertate the city of Zwolle of the remainder of the night.