The cast of Fullmetal Alchemist have so many recorded Berserk Buttons that it practically requires separate folders for each one.
Edward Elric
Perhaps Ed's most famous Berserk Button is any mention of his vertical deficiencies. He usually ends up exaggerating the insult to ridiculous extremes as well as whooping the ass of the offender.
The only one he won't go nuts on is Al (after all, they're brothers...and someone has to keep him in line), and even he got away with a knock on the head and a retort of "Don't call me small." Of course, the short rants are constantly a Crowning Moment of Funny.
Also, don't suggest that Winry is his girlfriend. At the same time, however, don't even think about harming a single hair on her head...because Ed will kick your ass. Like the narrator in Brotherhood says, he will do anything to protect her.
Threaten his little brother Al while Ed's around and you'll find yourself very, very, VERY soon regretting it.
It's also not too much of a good idea to bring up memories of the human transmutation incident for laughs, although this was more of a Tranquil Fury in the first episode of Brotherhood.
Ed: You know...there are some lines you really shouldn't cross.
The closest Ed ever comes to killing someone is when he has Shou Tucker up against a wall after Ed realizes he used Alexander and Nina for his chimera experiment. He might have let him go if Tucker hadn't decided to show us all what a bad idea it is to laugh at Ed's worst memory. He was on the road to getting pummeled to death with a steel fist before Al pulled his brother off.
Winry Rockbell:
Edward finds himself the victim of her Berserk Button whenever he needs to go back to Winry for maintenance and (predominantly) repairs. If there's even so much as one scratch...
Also, never criticize her handiwork. After hearing someone insult her automatic craftsmanship in the first anime, Winry went from telling Ed to calm down to telling Al to let Ed go so he could (more or less) kick the guy's ass.
Roy Mustang:
Much like Ed with Winry, it is a very bad idea to even imply that you might harm Riza Hawkeye. Your only chance of surviving such an implication is if he is heavily restrained.
Don't imply that you're attracted to her, either. In the manga, Barry the Chopper declares that he's in love with Riza (because she shot at him instead of screaming in terror). Then he makes the mistake of putting his hand on her waist, clearly against her wishes, in front of Roy.
Oh, and don't suggest that she really enjoys killing, like Kimbley did when they were all serving in Ishbal. Riza in a Corner of Woe makes for one really pissed-off Roy.
Gluttony is usually a Psychopathic Manchild who just doesn't get that eating people isn't very nice, but hurt his beloved Lust and watch him completely flip out.
Scar does not take well to anyone involved in the Ishbalan genocide. And "does not take well" means "will dissolve your head via Face Palm of Doom."
Ed and Al share a minor (in Al's case, not so minor for quite a while) one that is labeled "Pointing out how GREAT it actually is being a soul trapped in a suit of armor". It led to one pretty not-so-nice brother fight.
Don't mock Hohenheim's sons in front of him. Just...don't.
Any open or implied disrespect of Ling in front of his vassal Lan Fan will result in her giving a Death Glare to the person responsible, at the very least, or her attacking the offender.
Ling gets pretty pissed whenever someone, especially those in positions of power such as Fuhrer Bradley, try to convince him that leaders should be able to abandon their followers.
