Do NOT say you're the one who is gonna be Pirate King within Luffy's earshot (or at least not as mockery; he at least tolerates the ones he sees as rivals).
Taking his meat is also a fine way to piss him off.
Don't try to destroy a Jolly Roger. Wapol learned this one the hard way.
Do not attack, kill, or even disrespect your own nakama - even if they was Luffy's enemies, he will still end you for that.
Zoro destroyed Kaku after being at best evenly matched throughout their fight after Kaku called their efforts useless (though in the manga, Kaku said nothing). "Don't get too carried away."
Much earlier, it becomes clear that he doesn't take kindly to being accused of being unable to keep a promise. Due to the fact that his life's ambition is pretty much built off of a promise that he made to Kuina, this is understandable.
Do not spend money without consulting Nami first. Do not steal anything from her, especially if she stole it first.
Usopp is a Lovable Coward, and would rather run away than fight. But if you insult Luffy in front of him, you're doomed; he may be the weakest of the Straw Hats, but he's still a One-Man Army when he needs to be, and he won't put up with insults to his captain. Mr. 4 and Miss Merry Christmas found this out the hard way, after hitting him with enough force to kill a normal human a thousand times over.
Sanji's biggest berserk button is when anyone wastes food, including using food to fight with. He and Old Man Zeff almost died of starvation when Sanji was a child, so this one's very understandable.
A close second is if anyone mistreats a woman.
A third is his wanted poster. Don't bring it up, but if you do, do not say it looks like him.
A fourth one is weaponized by him in his "Hell Memories" attack. He brings up his memories from the two years he was stuck on an island full of transvestites and beats up his enemies with the rage from it.
Being a doctor and saying you are Only in It for the Money is not a very good idea to say within Tony-Tony Chopper's hearing.
Robin is also quite angered by those who disrespect history, as she demonstrates on Yama in the Skypiea arc. She also gets angry when people talk about her past and why she got her bounty often because what they're saying is not true.
Brook's afro is precious to him as it is the last defining feature he has that his old friend Laboon can recognize him by. So... Do. Not. TOUCH. THE. AFRO.
In One Piece Film: Strong World when man-eating ants ignore Brook because he was considered "leftovers", he angrily states it was "a bit inconsiderate" and proceeds to cut all the ants down. This Berserk Button is pushed again in Chapter 682, when the little dragon from Punk Hazard looked disappointed that Brook didn't have any meat on his bones. This actually serves as a minor plot point, as it reveals that Kinemon also hates dragons, but for a much darker reason.
Buggy the Clown. If you insult his clown nose, he will freak out, and given the chance, he will shoot you with a cannonball capable of destroying several city blocks. When you account for the fact that he tends to mishear things and assume they were insults to his nose…
Rob Lucci, Dragon-in-Chief of the CP9 arc. Typically, he's cold, calm, and collected, but he does not take kindly, at all, to mockery. And he's more than dangerous enough when he's not angry.
Portgas D. Ace can be seen as a deconstruction of this trope because in the Marineford arc, when he was rescued from execution, he let his emotions get the better of him. When Akainu starts to insult Whitebeard, Ace is drawn into a hopeless battle that ultimately kills him. This happened despite everyone, including Whitebeard, warning him to run away.
Gekko Moria has two notable ones. First is his old crew of True Companions, who were massacred by Kaido; just thinking about it is enough to provoke a Villainous Breakdown. Almost as big of one is stating, or even just implying, that he's weak.
If anybody mocked Eustass "Captain" Kid's dreams about becoming the pirate king, he wouldn't hesitate to straight out kill them for that.
Bartolomeo, a character who first appeared in the Dressrosa arc, was introduced as a rude, Ax-CrazyJerkass. It's bad enough if you provoke him at all, but he absolutely worships Luffy; say one bad word against him in this fanboy's hearing, and it will be the last thing you ever say.
Out of all people, Trafalgar Law's berserk button seems to be a massive one. If anyone insults, laughs at, or slights Donquixote Rocinante, a.k.a. Corazon, he noticeably loses his cool and flies into a violent, screaming fit. And God forbid if you actually kill him. After Doflamingo murdered Corazon, Law vowed to murder Doflamingo at all costs; his entire career as a pirate, thirteen years of it, has been focused on avenging the man who saved his life, even if it cost him his own.
Donquixote Doflamingo has two notable ones: people who would mock or insult his family in any way, and people who bear the name of D.
One of Doflamingo's top three executives, Pica, also has one: do not mock, insult, or laugh at his voice. And unfortunately, in spite of—no, because of the fact that he is a very tall, very muscular, and very powerful human, this button is pressed too often thanks to how little his high-pitched voice suits him. Heck, even Zoro was incapable of holding back his laughter.