This exchange from The Movie is pretty self-explanatory:
Naruto: Man, I don't know where you got your taste in men, Sakura, but it stinks. Sakura:(furiously) WHAT DID YOU SAY?! Naruto:(with Blank White Eyes and a small voice) I'm sorry, what was the question?
On a more serious note, even mentioning Orochimaru in a respectful fashion in front of Naruto is a good way to activate Naruto's Superpowered Evil Side.
After the timeskip, Naruto and Sakura are both angered by anyone who badmouths Sasuke, or suggests that he is too far gone for them to bring back.
Lee gets quite angry whenever anyone speaks ill of his mentor Might Guy.
Those examples are NOTHING compared to Naruto's biggest berserk button; killing or appearing to kill his friends. When Pain pushed that button in his legendary Moral Event Horizon in chapter 437, it triggered an Unstoppable Rage that would make the fury of the Incredible Hulk seem like a child's tantrum.
Also accounting for foreshadowing, this specific Berserk Button is what pushed Naruto through his firstUnstoppable Rage when Haku nearly killed Sasuke during the Wave Country arc.
Speaking of Naruto, you should never insult the title of Hokage in front of him. He won't care if you're one of the legendary sannin. He won't care if you're a woman. He...will...KICK...YOUR...ASS!
One filler arc pre-Time Skip gives Naruto another Berserk Button. An imposter is going around Konoha, ruining Naruto's reputation (and his good credit at the local restaurants). Worn out from trying to clear his name, Naruto starts to head home...then has a major Oh Crap moment and rushes all the way back there to find that the imposter ate his entire supply of beef ramen that he was stockpiling. Cue Superpowered Evil Side breaking out.
Initially, Sasuke's berserk button was simply mentioning his brother, now it's mentioning his brother in a disrespectful way.
Or if you mention his clan...or have a Sharingan "That you don't deserve".
Shikamaru may be the hardest guy to rile up in the entire series. You might see him irritated, but it's a rare thing to catch him genuinely angry for long. The first guy to do it gets hunted down, blown to pieces, and buried alive. Moral of the story: killing people Shikamaru cares about is a bad idea.
Don't mess with Gamabunta's sons or underlings, it's not a good idea, even if you're a tailed beast.
Very few things seem to bother Tobi (being immortal and all) but he gets pretty ticked off if somebody betrays Akatsuki. Of course he has quite the Freudian Excuse.
Interestingly enough, this might stem from the fact he is Obito, who highly regarded friendship & teamwork.
Kakashi REALLY hates Orochimaru and Kabuto's Edo Tensei (Summoning: Impure World Resurrection) technique, which they use to revive dead shinobi and force them to fight. In fact having to fight an Edo zombie is the first thing in the manga that visibly made him rage. In fact he really seems to hate Kabuto in general.
He also values his comrades, and dislikes people betraying their own. Notably, back during Land of Waves mission in Part I, Zabuza's repeatedly kicking Naruto (who is also Kakashi's sensei's son, mind) and belittling his students pushed him into quite the Tranquil Fury - once he was freed from Zabuza's Water Prison, the Death Glare he gave the Missing-Nin was quite impressive. Then, he handed Zabuza his rear end on a platter.
Another one, but anime only. Don't bring up Rin's death (unless you're Obito). If you do, then he will have no qualms doing exactly the same thing he did to Rin on you.
Aside from being a Stepford Smiler, Sai doesn't really seem to get fazed by much of anything, whether comical or serious. However, all that changes when his resurrected brother's body gets blown up by Deidara, who boasts that he can do the same thing as many times more as he likes. This is Sai's response.◊
Hinata doesn't like it when Naruto is in danger. She'll stare you in the eye and try to attack you even if you did just destroy the village.
Implying that those with a bijuu sealed in them is Not Even Human or the use of the term jinchuuriki by anyone who either a jinchuuriki or good friends with one is a major one for Naruto.
It doesn't take much for Deidara to flip a shit but if you call his art inferior (or a cheap rip-off)...run.
Don't ever claim that names don't matter to Kabuto.
The Nine-Tailed Fox, Kurama, really, really hates Madara. His mere presence was enough for Kurama to instantly offer an Enemy Mine team-up with Naruto.
It was understated at the time, but Kurama really did not like Pain's view of the world. It irritated to much that he inadvertantly synchronized his own chakra to match Naruto's and the natural chakra Naruto had gathered just to have a part in the fight. doubles as Exotic Eye Designs, because his fox eyes overlapped with Naruto's frog eyes to give him some kind of freaky orange cross eyes.
Do NOT mention the 1st Hokage around Madara.
One other Berserk Button for him: Don't stand behind him when he pees, it irritates the hell out of him. Something Hashirama was fond of doing, just to get a rise out of him. No wonder he hates the man to this day.
Don't call Yagura a kid. He may look like one, but he's actually an adult and the Fourth Mizukage as well.
Threatening Konoha in front of Tobirama aka the Second Hokage is a bad move. It made Orochimaru, Sasuke and Suigetsu freak out by his Death Glare alone. You better hope that Hashirama/First Hokage is there to stop him.