Mild spoiler warning for characters you wouldn't expect to get angry!
From Naruto: Shippuden
Sakura is by no means an unfriendly person, but boy does that girl have a short fuse. Combined with someone who is as dense as Naruto, she gets ample chances to deal out some punishment. You would think Naruto would eventually learn not to tick off the woman who can punch through buildings with her bare hands.
From Dragon Ball Z
Hell hath no fury like a woman scorned, and that is especially true when the woman is your wife. It should speak volumes that Son Gokuu and many other members of the Z Fighters are openly afraid of this normal(ish) human woman despite all of them being powerful enough to destroy planets with a flick of the wrist.
It takes a lot of killing to earn a nickname like Battousai the Manslayer, but Kenshin Himura did just that. While the terrors of war did cause Kenshin to take a vow against killing, you cannot go through a nightmare like that without becoming a little unhinged along the way. It can take a lot to make Kenshin angry but when that does finally happen, God help you.
A classic example of a tragic hero, Guts began his life from death as he was born from the corpse of his mother. Being trained as a soldier literally from birth, his life has seen little more than one battlefield after the next. A lifetime of killing has given Guts a "swing sword first, ask questions later" attitude and his heart hardens further with each comrade that is lost.
From One Piece
Luffy is a really nice guy. One of the nicest you could ever meet. He does not kill people, he goes out of his way to help others and do the right thing, the whole shebang. On top of all that, he cares about his friends more than anything else. So if you are unfortunate enough to have hurt one of his friends, run. Do not try to fight; just run. It is the only chance you have. The nicest guys have the strongest anger buried within and Luffy is one of the top examples of that.
Sometimes anger is an involuntary choice. You do not choose to get angry, it just happens to you. For some people this is just how their mind works but for Ichigo Kurosaki it is because he has a literal inner demon that is happy to come out and kill, kill, kill.
You know what really grinds my gears? When I am trying to take over the world by fighting the planet's largest military power and things just are not going my way. Staging a rebellion is not easy, it makes a lot of hard work and dirty manipulation. Honestly, my plans of global conquest having even the slightest risk of failure can be such a stress inducer.
From Mirai Nikki (TV)
Ah, the girlfriend who would do anything for you. From keeping you company for the day to bringing you soup when you are sick, from defending your honor to insulting other girls who come near you...wait is that a knife? She's got a gun too! Yeah, crazy angry + weapons is not a good combination for anyone else who happens to be standing nearby.
From Tottoko Hamtarou
Anger can take many forms, even little cute and tiny. Sure Chibimaru-chan is furious, but is she not still adorable? Look at that face, how could you ever be angry with a rage-induced hamster face like that?
Sometimes anger is used to cover up another emotion, such as embarrassment. The angry person will still totally clobber you in this state and you might also even make them cry. Way to go, you monster.
From Fairy Tail
Some protagonists gain their strength through the power of friendship and love, whereas others just get really pissed off and keep hitting you until you stop moving. When someone has the amount of literal firepower that Natsu can wield, it may be a good idea to stay on his good side.
From Cardcaptor Sakura
When you are angry you just want to punch and kick and...cook? Well I guess everybody needs an outlet, and even if you are angry that does not mean you have spare time to neglect your chores.
From Plastic Neesan
Ever been so mad with someone you grabbed them by the face and slammed their body into a wall hard enough to shatter the stone it is made from? No? Ah anime, never change.
From Yuru Yuri
One of the most extreme physical examples of anger is becoming red in the face. Not like, "oh you look cute because it looks like you're blushing." More like, "blood is going to her brain for extra processing power so she can simultaneously plan how to kill me and where to hide the body."
Nothing quite triggers an angry spell like a complete and total mental breakdown, where there is certainly no shortage of in Higurashi no Naku Koro ni.
Almost everyone has had that moment in life where the vending machine just refuses to work. Maybe your snack gets stuck on the way down or maybe the machine ate your coins, but something went wrong. It is at this point where the vending machine voids its rights to physical safety and you have determined you are free to do whatever you want to that machine because darn it you need your snack!
Very few things can spark a murderous rage within a man, but coming face to face with his best friend's killer will certainly due the trick.
From Soul Eater
Most girls learn a simple fact about boys at a young age; boys are stupid. With a dork of a partner, Maka often finds reason to inflict physical harm on her friend Soul.
The angry girlfriend who won't even look at you and probably doesn't return your calls. Kagome Higurashi has the stubborn anger of the teenager that she is, which makes matters worse for Inuyasha as he is saddled with an unremovable magic necklace that she can use to slam him into the ground hard enough to leave Inuyasha-shaped holes.
From Dai Mahou Touge
Self-mutilation is a grotesque and horrific act, but it becomes hilarious when an animated potato is doing it. Taking a deadly vegetable peeler to his own skin, the intense emotions felt by potato result in an action of bravery, courage, and a delicious lunch.