Well, in Katekyo Hitman Reborn!, this is pretty much what Reborn tries to teach Tsuna, which is part of his process of growing out of being a total loser and becoming a real man. The Dying Will Bullets, to put it simply, either put Tsuna into a determined, unstoppable rage, or give him cold, calculating killer instinct. This is mainly played as having good results, with Tsuna gaining a backbone and the strength to protect his "family."
There's a Star Wars manga (yes, Star Wars manga, and not just of the movies, although it's non-canon) where Darth Vader slaughters a colony of hidden Jedi and spares the last one, a rather young boy, because Force Sensitivity plus incredible anger equals a good Sith apprentice. So Vader takes the boy back and finds that while Tao attacks him on command, for whatever reason even reminding the boy that Vader killed his family and razed his world doesn't make him use his hatred. ...It's a rather weird story.
Gohan pretty much goes through this in the Cell saga of Dragon Ball Z. It has good results when he finally achieves the Super Saiyan state, but when Cell forces him to go Super Saiyan 2 so he can have a worthy fight the opposite happens. Crowning Moment Of Awesome yes, but Gohan's actions later on cause Goku to make a Heroic Sacrifice.
A large part of Gohan's training with both Piccolo and Goku is this. It finally culminates with Android 16 summarizing it in a succinct speech right before Cell kills him. The result gives Gohan access the Super Saiyan 2 and the loss of his childhood innocence, only for him to forget how to get the most out of channeling his rage 7 years later when it's needed again, and simply being out of shape.
Zane in Yu-Gi-Oh! GX. After a string of crippling defeats, he ends up on the brink of losing to a comic relief opponent while the crowd makes fun of him, and his manager coaxes him to let go of his "failed" ideals that got him to this point. The kid goes berserk, summoning a monster that almost destroys the arena and takes out his opponent in one turn. The whole point of this duel was for Zane's manager to convince him to reform and turn his career around, but if his reaction to Zane's gambit is a good indication, this wasn't quite what he had in mind.
In Fist of the North Star, Shin unintentionally does this to Kenshiro. After thoroughly defeating him, Shin gloats to Kenshiro that the difference between the two is that Shin is filled with ambition and Kenshiro isn't. Kenshiro took this to heart, and by the second encounter it's the other way around, with Kenshiro burning with anger and ambition to save Yuria against a broken Shin from Yuria's apparent suicide. The fight barely lasted 10 minutes.
One Axis Powers Hetalia strip has Greece trying to get the polite and soft-spoken Japan to become angry. He succeeds by telling him to think about wasting his money.
In Pluto, Dr. Tenma teaches Atom hatred in a desperate attempt to awaken him from his coma. It works, and the extra hatred gives Atom the ability to fight Pluto.
Atom: You may be a seething mass of hatred. But my hatred is greater by far.
As it would turn out, Tenma also gave Atom Gesicht's dying memories presumably to give him more hatred. As it turns out Gesicht's final moments were so anti-hatred, it inspires Atom and Pluto to work together to save the world.
Guilty's training of Ikki in Saint Seiya, giving him Training from Hell while goes to extreme levels to anger him to use the Phoenix Cloth. Ikki endures it all until Guilty accidentally kills his own daughter Esmeralda during training, making him snap and kill Guilty in a fit of rage (to Guilty's glee), earning the Cloth in the process.
The whole first half or more of Trigun is about this trope being pushed on Vash, the villains trying to make him snap and kill. Knives' whole life has been theoretically devoted to a Roaring Rampage of Revenge against the human race, and he wants his brother to join him, or failing that to stop being so high-and-mighty.
Wolfwood, who isn't a villain even if he is working for them, is even more determined on this front; in the manga this leads to an epic moment where he pulls Vash's gun against his own face and demands, "shoot." Saying it would be worth his life if Vash would submit to reality and take up his role.
Vash does have plenty of anger, and on occasions like 'Diablo' it proves seriously scary. He wins the really important things without it, though. Both versions.
Played with in Naruto when Pein stabs Hinata in front of Naruto to "teach him pain" and prove that humans can never really understand each other. He's convinced that his pain is stronger than anyone else's so Naruto's resulting fury is no threat to him. He's wrong.
Bruce Banner has Aesop Amnesia about this. The Hulk, of course, doesn't need to be taught anger. But the Hulk is usually considered a product of Banner's repressed rage, childhood abuse, and generally screwed-up psyche. Trying to control or get rid of the Hulk usually involves helping him with those issues, often meaning not bottling things up so much. Sometimes this results in fewer Hulk episodes, sometimes it results in a smarter Hulk, and at least once it resulted in a Banner with the Hulk's strength.
"I see pride! I see power! I see a bad ass mother who won't take no crap off of nobody!"
Something of a comedic subversion: As Junior takes the lesson to heart and storms off to confront his father, Yul quietly that he was actually talking about himself not Junior but, hey, if it works for the kid...
In the Disney version of The Reluctant Dragon, the boy tries to get the dragon to breathe fire, but can't because he needs to be mad to do so, and he's not mad at anyone. It's only when the boy insults his poetry that the dragon starts spewing flames.
In Star Wars Episode III, the Emperor did to Anakin. In Star Wars Episode VI, he tried to do to Luke. (Luke falls for it twice, but the third time he refuses to attack, and is promptly fried by a disappointed Sith Lord.)
Star Trek XI. Definitely example #2, as ALL Vulcans possess a violent beast beneath their calm exterior (and they're a lot stronger than humans). So, pushing Spock, who had just lost his entire planet (including most of his species and his mother), while necessary, was very painful for Kirk. Verypainful.
This is the means by which the bad guys seek revenge against Mr. Miyagi by transforming Daniel-san into the opposite of everything Miyagi taught him to be, in Part III.
In Dodgeball, Patches tells the timid, nerdy Gordon that he'll never be a good player until he learns to get angry. During the tournament, Gordon sees his mail-order bride with another man, goes into a rage, and single-handedly brings the team back from the brink of defeat.
Wizard's First Rule has Zedd teach Richard how to channel his anger instead of surpressing it, which allows him to use the full power of the Sword of Truth.
Emperor Mage, the third book of The Immortals quartet, Daine learns to use her anger to focus her power, though admittedly she has plenty to be angry about already.
In Carpe Jugulum, the Magpyr family are vampires, the patriarch of which has extensively trained to resist all the classic vampire weaknesses because he doesn't see why they have to do it the stupid way and lose some of the time when they can win all the time with training. When the old Count de Magpyr returns, he's encouraged to take his grandchildren under his wing and teach them stupid, because biding your time, dead, for a few decades, is how a vampire really gets ahead.
Dialed Up to Eleven in The Fionavar Tapestry by Guy Gavriel Kay. The race of Giants are the ultimate pacifists, unable to hate and unwilling to defend themselves. All but one refuse to even so much as ask for aid when they are being slowly tortured to death, because it would mean someone else has to battle on their behalf. When they are rescued from the brink of extinction, they are still unable to hate on their own behalf — only being forced to witness the brutal rape of someone else finally undoes their absolute pacifism. And even undone, they still never shed blood or directly fight in any way.
The novelization of Revenge of the Sith makes the Sith efforts to do this to Anakin more explicit - Count Dooku thinks that the plan is that he kills Obi-Wan, then Darth Sidious talks Anakin into joining the Sith, then Dooku surrenders and gets to sit out the war and become part of the developing Empire. It doesn't work quite like that.
On 30 Rock, Kenneth of all people takes it upon himself to push new guy Danny Baker to anger so that he doesn't get stepped on by Tracy and Jenna.
Doctor Who. One of the Doctor's companions does this to the Thals to show them there are some things they're willing to fight over. The Thaals had previously been willing to be exterminated by the Daleks rather than break their pacifist ways. 
The "bad outcome" of this occurs in an episode of Farscape, "That Old Black Magic." Zhaan must revive her old sadistic anarchist ways in order to defeat Maldis. It takes her several episodes to fully regain her self-control.
In one fourth season episode, where an evil spider alien stole the most important aspects of the main cast's personalities (John's determination, Aeryn's self-control, Chiana's sex drive, Rygel's greed, D'argo's anger), Chiana proves it by trying to teach D'argo anger again by beating him up. It doesn't work, which is a really big problem.
Star Trek: The Original Series has Kirk have to anger up Spock (who's on the feelgood spores) and then let himself get smacked around by an enraged Vulcan until he gets it all out of his system.
Buffy the Vampire Slayer. In "Get It Done" Buffy has to do this with both with vampire Spike (after he got a soul) and witch Willow (after briefly turning evil at the end of the previous season). At the same time over on the Angel spin-off, Wesley has to do the same thing with vampire slayer Faith, who also turned evil and was now regretting it.
Alphas plays with this in a very complicated way. When Bill trains with Kat in the second season, her training is mostly based around getting him to relax so that he can access his superstrength without having to force himself to get angry. The reason why this isn't a straight reverse example is that it's strongly implied that the reason why he had to get angry in the past was down to inhibitions and guilt about being violent, and that the training has also reduced his inhibitions about violence in a way that might not be entirely positive.
Jade Empire allows an evil character to do this to Dawn Star.
This is part of Master Xehanort's plan in Kingdom Hearts: Birth by Sleep. After seeing Terra lose his cool during the Mark of Mastery Exam he sets up a plan. After disappearing he sets up an encounter with Maleficent to make his friends question his hold over the darkness. Afterwards Terra is convinced to hunt down Vanitas and stop the darkness in his own way knowing his friends would not understand. During this Xehanort sets up the climax. By setting him up to defeat Master Eraqus, the last thing that would stop him and throw Terra off the slippery slope at the same time. Terra loses it and defeats the Corrupt master, however all had gone according to plan for him, Terra had lost himself to the darkness and he was then ready for Xehanort's Grand Theft Me.
In Planescape: Torment, the Nameless One can teach an NPC how to get angry. The goal is to get her annoyed enough at her co-workers to gossip about them, though. It's a noteable Crowning Moment of Funny in a game that was already full of them- you have to start by getting her to "practice" insulting you, which she does by first telling you that she thinks that you're a less than perfectly wonderful person, then working herself into a full-on scenery chewing rant.
In Sword of the Stars, the second variant describes the training of Black Swimmers. The Liir are a species of Empaths who are pacifistic as a result, but because they need to defend themselves somehow a special caste of volunteers known as the Black Swimmers keep them safe by teaching themselves how to hate and kill. Black Swimmers are basically irredeemably Ax-Crazy by Liir standards and both sides are all too aware of this, but are nonetheless necessary for the race as a whole to survive. Their Initiation Ceremony involves 'drowning' the aspirant in liquid oxygen until they black out and abandon all hope.
In Phantasy Star IV, the main character can go to the Anger Tower and learn, arguably, the most powerful technique in the game, which happens to be fueled by anger; this trope comes into play when Re-Faze puts Chaz to a Secret Test of Character: forcing him to confront and then kill a specter of his deceased mentor and surrogate mother, and then taunt him for his pain after realizing it was an illusion, then offer to teach him the Forbidden technique to taunt him with how incredibly powerful it would be.
The Beast does this to Will in Days of Ruin in order to make him a satisfying opponent. His method of doing so? Killing civilians. It works well enough that the Beast is never seen again after that mission (presumed dead based on Caulder's lines).
Namco High: the Meowkie path involves helping her deal with anger in a healthier fashion than repressing it and pretending she never experiences it. Then, during the final battle against Evil Namco High, she deals with it in very cathartic fashion by shredding the evil robots.
Tower of God: Baam, for the life of him, could not conceive any reason why people would fight. Rachel asked him what he'd do if somebody hurt her. He then understands.
Headon takes this to the next level when he tells Baam that he won't see Rachel ever again if he doesn't take that test. This is more a case of evoking Baam's greatest fear. Headon being Headon, he doesn't mention that Rachel is in an adjacent cavern watching them.
In the "That Which Redeems" arc of Sluggy Freelance, Torg tries this to multiple characters in the Dimension of Lame in order to get them to defend themselves against the demonic invasion. He fails; the people in the Do L are so pacifistic that even a character who would be Axe Crazy in any other dimension can only manage to pound one demon on the foot with a hammer before breaking down into What Have I Done.
In The Order of the Stick, when Belkar recovers from his coma, he and the cleric hired by them to contact Durkon (the same one who healed Belkar) cut their way to the front door killing the Thieves Guild members swarming the place. There they encounter Old Blind Pete who betrayed them. Due to his fake Character Development, instead of killing him, he leaves him to the cleric instead (who were childhood friends with Pete). The cleric first says that he doesn't do such things, but then gives in and kills Pete. He even delivers a Pre-Mortem One-Liner. Of course, Belkar being an Anti-Hero / Villain Protagonist, he is just happy to have made a heroic character more anti.
Punchline: When you were adding the numbers up, did you remember to carry the stupid? Anarch:Yes! ...no.
In Red vs. Blue, Caboose (a very nice, but exceptionally dumb member of Blue Team) was possessed by the AI O'Malley. Later, Caboose and Sarge are fighting two armies of flag-worshipping zealots. Caboose claims that "O'Malley taught me how to be mean"; by concentrating on things that make him angry (red bull, kittens with spikes on them), he proceeds to go crazy and wipe out both teams; before waking up with no recollection of his actions.
Caboose never really displayed that sort of capability afterwards. Until Episode 21 of Season 10. When facing an army of Tex copies, Church needed Caboose to get angry; and Caboose revealed that he forgot how. Church helped him remember.
Family Guy does this when Peter decides to train Cleveland after his wife leaves him for Quagmire. It has unfortunates results as Cleveland rampages around Quagmire's house chasing him and revealing beds that pop out whenever he hits something. Hilarity Ensues but Cleveland finally snaps out of it (after a Return of the Jedi makes him realize what he's doing) and goes back to being his old self.
In "Patriot Games", Peter tries to do this with a team of stereotypical British boarding school types. In a deleted scene, he hits on the solution of showing them the American version of The Office.
Storm Hawks has Junko pose as a wrestler to get the team into the Cyclonian's enemy base. Since he's normally a Gentle Giant, Piper uses a hypnosis crystal to give him a confidence boost. She then gives it to Finn along with instructions to only use it sparingly, along with the code phrase to turn off the conditioning should an emergency arise. Finn of course uses it so strongly Junko actually believes he is the Masked Masher and can't recognize his friends. It all comes to a head when Master Cyclonis puts them all in a cage match against the Brainwashed and Crazy Junko. Luckily Piper manages to remind Finn of the code phrase.
Toph: Rock is a stubborn element. If you're going to move it, you've gotta be like a rock yourself.
Inverted with... Well, EVERYTHING Uncle Iroh was trying to teach Zuko. Pretty much every other proud Fire Nation warrior used the purely aggressive style of fire bending, meaning Teach Him Anger was more or less Class 101 in the academy. Iroh and Jeong Jeong were among the few that realized that was self destructive, not just on a personal level but for the entire nation in the long-term.
In the ninth The Land Before Time film The Big Freeze, Ducky asks Cera this, who delivers it in song.
Accidentally invoked by Megatron on Beast Wars when Scorpinok's mind-altering bug took away Optimus Primal's self-control and inner peace. His reasoning was that Optimus' calm exterior was a facade for a cowardly streak, but in fact it was a safety mechanism to control his Unstoppable Rage. With his inner peace removed, Optimus goes on a Roaring Rampage of Revenge, taking out the entire Predacon force single-handed before the Maximals manage to remove the bug that was slowly killing him. Beware the Nice Ones indeed.
Plankton attempts to invoke this on SpongeBob SquarePants as part of a Batman Gambit to make Goo Lagoon a site for a new Chum Bucket. Spongebob, in response, decides to be "aggressively nice".
Dexter, from Dexter's Laboratory. In one episode, Deedee encourages the titular character to see how good it feels to break stuff, but he goes mad and Deedee becomes terrified of how destructive and psychotic he became, and she gets him to revert back, apologizing and saying that maybe it's better he remains emotionless.
In Codename: Kids Next Door, Numbuh Four is trapped on an island with a giant rainbow monkey who would rather hug and kiss him than pummel him. Numbuh Four then tries to teach the monkey how to act ferocious, but becomes increasingly frustrated when it doesn't seem to work. After Numbuh Four is finally rescued, the giant rainbow monkey follows them home to get him back, and is now extremely pissed.
Numbuh Four: Maybe he was paying attention to me.
In The Simpsons episode "Hurricane Neddy", Ned Flanders suffers a mental breakdown in which he furiously chewed out Springfielders as a whole, and checks into a mental hospital. His psychiatrist Dr. Foster realizes the best way to help him out of his breakdown is to have him intentionally angered by the person who annoys him most, namely Homer.