When a nice, normal character suddenly goes into a rage, you've hit his Berserk Button.
Of the various Clans in BattleTech, the Ghost Bears are frequently considered to be the most laid back and least aggressive. Unless you attack their capital, Alshain. Or use nuclear weapons. Or they have any reason whatsoever to even suspect that you might be associated with Clan Wolverine. Doing any of the above makes them angry. That's very, very bad.
While the Diamond Sharks would rather sell you weapons than shoot you with them if you attack their mercantile interests or civilians you are in for a beating. When the Draconis Combine was trying to acquire advanced technology after most of their production centers were destroyed in the Jihad, they went to the Sharks. The local warlord gave them a continent to set up shop but a few of his senior officers took offense to this "Clan occupation" and killed a few hundred civilians. By the time the warlord managed to call his subordinates off, the Combine had lost two regiments.
For most Clans they consider having non-warrior castes taking up arms as abhorrent, when it is discovered that Clan Blood Spirit one of the smallest clans was using armed militia to bolster their forces, the remaining clans call for the Blood Spirits annihilation.
Tabletop Game/Earthdawn. Each ork has certain specific things (situations, topics of conversations, actions, etc.) that can trigger a terrible rage in them, which usually leads to violence. Some examples of this type of trigger (called a "gahad") are slavery, infidelity, family loyalty, competence at a profession, pastimes or favorite hobbies, possessions, who's really in authority, Horrors, politics and the Theran Empire.
Exalted: Even if an Exalt fills their Limit meter, it's not necessarily enough for them to go into a Limit Break. Rather, each Break comes with a trigger condition, such as "Annoyed at the childish nature of the world" or "Witness an act of suffering that you could easily stop." A good example of this trope in its pure form is the Red Rage of Compassion break, which typically involves a normally kind-hearted and compassionate Solar going into an Unstoppable Rage after seeing one too many innocents cut down.
The "Consumer On the Brink" archetype from the Feng Shui supplement "Seed of the New Flesh" is not very powerful in terms of skills. But attack him or put him in close proximity to his irritant, which is a Berserk Button or something else that pisses him off to no end, and he gets 4 bonus points that he can distribute however he wishes between his Body and Reflexes stat, which can affect his combat AVs.
GURPS has multiple was of simulating this on a character, the most common of which is simply called Berserk.
Old World of Darkness - If you ever cross paths with a member of the Sabbat on the Path of Honourable Accord, don't ever, ever, ever, EVER accuse them of breaking their word. They will pursue you with the full fury of a raging vampire until you either apologize, die, or kill them.
Clan Brujah has this as their hat. Almost every Brujah vampire has something that throws them off in some way... or in some cases, almost everythingpisses them off. Some are more easily pushed than others, but even the calmest elder of the clan has something that pisses them off — and you don't want to be anywhere in the general vicinity if that button gets pressed.
In Paranoia, avoid being a Communist. Friend Computer will allow mutants to register their powers, and may even be lenient on traitors. But if you are a Commie (or made to look like one), you WILL be terminated.
To make lycanthropy less predictable, Ravenloft encourages Game Masters to link werebeasts' involuntary transformations (and subsequent Berserk Button rampages) to phenomena other than the full moon, such as the tides, exposure to a particular odor, food or substance, or stressful situations such as feeling hemmed in by a crowd.
In Unknown Armies, the Rage Passion that all characters have is that thing that really sends a character into pissed-off rage mode. As Passions are perhaps the deepest part of an Unknown Armies character and the character goes all spooky-intense when put into situations that trigger one of the Passions, the Rage Passion is very much a dramatic Berserk Button.
Warhammer: Dwarves take their beards VERY seriously. The War of Vengeance kicked off when a Dwarven emissary was shaved by the overly arrogant elven king for his own amusement, which was the final straw leading to the breakdown of already-strained relations between the Elves and Dwarves in general. By the way, it is also not recommended to refer to that particular war by its elven term, "the War of the Beard", within dwarven earshot.
Mechanically speaking, if Vlad von Carstein sees his wife Isabella killed on the battlefield, the result involves an ancient and powerful vampire lord flipping his lid on an epic scale and attempting to individually kill everyone in the other army.
The Arco-Flagellants in Warhammer 40,000 are designed specifically to turn into berserk killing machines with the proper command. Don't examine them too closely, either. Bring up the Squats at any GW event, and you'll find that the Berserk Button works in real life, too.
Mentioning the horrible fanfic Squad Broken is a general berserk button for the fan base.
So anyway, what happened to the Squats? *duck and cover*
Eldar: In peace, they're gentle, logical, at-one-with nature, etc, with peaceful, quiet occupations. In war, they turn into furious killing machines, losing their identity to the overwhelming desire to annihilate the enemy. Oh, and if you steal or destroy Eldar soulstones, they'll hunt you down and destroy you and everyone and everything you've ever known and loved.
Suggesting harming civilians in front of the Salamanders is a bad idea, even if you're a chapter master.
Also concerning the Tau, Gue'vasa auxiliaries are a Berserk Button for the Imperium. So much so, that Imperial units get a close combat bonus against them.
Black Templars: Shoot one their battle brothers, the entire squad comes charging at you. This had led to comparisons with Berserkers of Khorne (to who, technically, everything is a Berserk Button (but Slaaneshi followers even more so)).
Cowardice is Khorne's Berserk Button. Slaughter defenseless women and children too much? He'll think you're a spineless pussy and set his hounds on you.
The Demon prince Graz'zt is probably the least likely demon lord to rip you apart just for existing, even opening his layers of the abyss for trade. Mention that he actually fell in love with Iggwilv, that Malcanthet turned him down, or call his domain "The Little Hells," and he will feed you to the predatory plants in his gardens.
In 4th Edition, suggesting that a half-orc was a Child Of Rape in earshot of one is a quick way to get your teeth punched out.