Mephisto from Blue Exorcist, who wants to make Rin strong enough to defeat Satan and (supposedly) bring peace to both humans and demons. He does this by repeatedly putting Rin in difficult, life-threatening situations—even sending the demon prince Amaimon to try and kill him.
Kisuke Urahara acts like this when training Ichigo in Bleach. His methods of training tend to mean death if failed. If Ichigo doesn't dodge an attack, he dies. If he doesn't look inside himself for his powers, he dies. If he fails to knock Urahara's hat off, he dies. Seriously.
Urahara also has a tendency to screw with people just for the hell of it. When beginning training, he gives Ichigo a helmet and claims that Ichigo needs to yell "TAKE THIS! THE POWER OF JUSTICE! JUSTICE ARMOR! JUSTICE HACHIMAKI! ATTACK!" When Ichigo does so almost instantly, Urahara mutters, "Wow! I can't believe he actually said that!"
Possibly justified in that while Urahara certainly enjoys being a dick to Ichigo, in the first example he genuinely thought that if Ichigo died, he wouldn't be able to make it into Soul Society in the first place.
Despite being mean, this did some good, occupying Ichigo's mind with something and letting his instincts do their thing. Yes, he performs worse when he actually tries.
In Fullmetal Alchemist, Izumi Curtis' idea of training is abandoning the Elrics on an island for a month and unleashing a monster (although it is later revealed that the "monster" was a shop assistant) on their tails. All for them to find the meaning of the philosophy behind alchemy.
Izumi is an odd case since she learned this method from her mentor, who was merely a survivalist who misunderstood what kind of training she wanted. She adapted it to be more suitable for alchemist training herself.
Oddly enough, the Truth is also this to the Elrics, especially Ed. It's genuinely pleased when Ed finally figures it out.
Jiraiya from Naruto adopts the "thrown in at the deep end" method of training. Literally. Unsatisfied with the hero's progress at accessing his power, he throws him off a waterfall.
Sometimes, the blacksmith Totosai towards Inu Yasha. Though other times Inuyasha just misunderstands what the blacksmith asks of him as training.
It has been argued that Genma Saotome and Happosai from Ranma ½ are this sort of mentor - putting Ranma through humiliation and hell for the express purpose of teaching him to be a superior martial artist. Genma steals Ranma's food? Defense training. Happosai tries to make Ranma wear lingerie? Teaching spiritual detachment. Or it could be that they're both dicks, which is the general view of the other characters.
Cologne has some of this as well, but her Training from Hell is always well-intentioned, and her students are very quick to catch on that both the training and the objective are equally useful. Then again, she sometimes pokes fun at the youngsters for the hell of it. Or because her cafe is overstocked with rancid noodles and can't think of any other way to get rid of them.
Jack Rakan of Mahou Sensei Negima! is like this. His training techniques include things like "Make a really ugly face and do 100 punches!" and "Punch me as hard as you can!". Yet, Negi still manages to learn Black Magic under his guidance.
It should also be noted that Rakan trains himself like this, too. After demonstrating said Black Magic, he reveals he had never actually tried it before, instead just being sure it'd work, and that he wouldn't be killed as a result of using it.
Initial D has Bunta Fujiwara, who secretly trains his son Takumi's road racing skill through years of tofu delivery runs on Mount Akina. And these aren't just any tofu delivery runs; Takumi is also given a cup of water to put in his car's cup holder, and must complete his run without spilling a drop of water. And then in Initial D Second Stage, Bunta invests in a new engine for the Trueno, but deliberately waits for the Trueno's original engine to break down in the middle of a race so that Takumi would be more accepting of the swap.
One Piece: Some might say Luffy's grandfather is one as well considering his training techniques to make Luffy a great marine, however, since his reasoning was make clear and it backfired big time it could just be Training from Hell.
The masters of Ryouzanpakou do this to Kenichi all the time. Their favorite technique is to focus training on one main task that is completely impossible, so that Kenichi will be so focused on that failure that he doesn't notice any of the progress he's made.
This is the preferred method of Hayato Furinji (a.k.a. The Elder). Akisame also often uses it. Other masters not so often, especially not Apachai who teaches very directly.
One very twisted example is the relationshp between Askeladd and Thorfinn in Vinland Saga. Askeladd sees himself is this towards Thorfinn, but Thorfinn hates Askeladd with a burning passion, and would sooner die then admit he had any such relationship with the man.
Hattori in Bakuman。, long after he's no longer actually Ashirogi Muto's editor.
Clow Reed mostly by way of Eriol Hiiragizawa in Cardcaptor Sakura. He has no issues leading Sakura and his own creations to believe that a danger is very real, only to reveal after they overcome it that there never was any risk.
In Nagasarete Airantou, main protagonist Ikuto has a Stealth Mentor (literally, even; Ikuto had no idea who he was, at first) in the West Leader, one of the Four Leaders that govern the island, and arguably the strongest of said four. When the West Leader finally reveals his identity to Ikuto, he quickly swerves into this type.
In Durarara!! a very, very generous interpretation of Izaya's character places him as one of these. His favorite hobby is messing with people's heads, manipulating them into going through emotionally devastating circumstances, seemingly For the Lulz. However, the ordeals Izaya puts people through often force them to confront some ugly truths about themselves, as Izaya is happy to point out. They may not be happier, but Izaya's victims are often wiser for having been used by him.
In many ways, the Silver AgeSuperman was one of these, particularly to his pal Jimmy Olsen and his girlfriend, Lois Lane (as well as his various other girlfriends). There are countless stories where Superman puts his loved ones through various sorts of Hell in order to teach them lame moral lessons. For Jimmy, the lessons often boiled down to "don't drink things you're not supposed to;" for Lois, they usually were "stop trying to find out my secret identity/trick me into marrying you." For the readers, the lesson was "Superman is a dick."
The Super-Teacher From Krypton was a robot built by Jor-El to teach his son. Of course, then the planet blew up... but by a fluke, the robot survived (a lot of Kryptonian stuff survived in the Silver Age) and eventually found Kal-El as a teenager on Earth. The robot took it upon itself to guide him in the wise use of his powers. The robot appeared twice, once in the Silver Age and then once in the Bronze Age. In both cases, it acted like an incredibly high-handed and manipulative Jerk Ass, and while Clark had to admit he had learned valuable lessons from it, he was very glad when the wretched thing took off back into outer space. So maybe this is where Supes picked up these same qualities when "mentoring" people as an adult.
John Constantine the Hellblazer is a mentor to Timothy Hunter in Books of Magic. Because of John's profession as con man, he sometime pranks Tim, sometimes to the point of endangering the kid's life.
The Red Dragon from Bone is a pretty low-key example; but it's especially noticable in the early parts of the comic, where he in between his lazing around and Big Damn Heroes moments will occasionally do some pretty weird things, either to teach the protagonists a lesson or just mess around with them.
Fone Bone: The dragon's doing this! He wants you to think he doesn't exist!
The Red Dragon:(Pokes his head out of a well) Actually, I just want her to think you're nuts.
Willy Wonka in Charlie and the Chocolate Factory is a variation. Gene Wilder, who played him in 1971, beautifully summarizes this trope with the story of agreeing to do the film on one condition: he wanted to make his entrance with a cane, limping, then suddenly somersaulting, "Because from that point on, no one will know if I'm telling the truth or lying." The director agreed to it, and the rest is history.
In The Grifters, Roy Dillon (John Cusack) finds a Con Man and asks to be taught how to be a grifter. The man agrees and gives him some advice. At the end of their conversation the man asks Dillon for $10. After Dillon gives it to him, the man says "Come around tomorrow, I'll take you again."
"The Old Man", of The Golden Child, played by none other than Victor Wong, who would later go on to play Egg Chen in Big Trouble in Little China. His first appearance to Eddie Murphy's Chandler Jarrell has him pretending to be a Tibetan street vendor selling junk jewelry, and scamming Jarrell out of money as a Secret Test of Character.
Likewise, the Dealy Lama (no misspelling). Both more or less good guys who make extreme effort to appear unreliable or even dangerous and evil to their wards. When you manage to connect the dots, you'll realize that the Dealy Lama was this trope: he inspired the myth that would become the Devil-character of every mythology in existence, including the Discordianism - about himself!
Terry Pratchett's Discworld novel Thief of Time includes Lu-Tze, a deliberate pastiche of Mr. Miyagi style trickster mentors. In true Zen form the humble sweeper Lu-Tze never quite lets on whether he's a profoundly enlightened wiseman with reality-defying martial arts powers or just a wiseass who gets by on audacity and luck alone. Right up until the end, when it is revealed that he's the former.
It is impossible to describe the Quintarian deity known as the Bastard from Bujold's Chalion books, Paladin of Souls in particular, as anything but this.
Ista: "What training? You never explained anything."
Bastard: "Instructing you, sweet Ista, would be like teaching a falcon to walk up to its prey. It might with great effort be done, but one would end with a very footsore and cranky bird, and a tedious wait for dinner. With a wingspan like yours, it's ever so much easier to shake you from my wrist and see you fly."
Bastard: "No. Not You. Granted, you tumble and complain halfway to the abyss, but eventually you do spread your wings and soar."
Hasan ibn Sabbah in Vladimir Bartol's Alamut, with the twist that he usually has the followers who realize that he is a trickster covertly killed. When one of them survives and comes back for revenge, he declares him as his own son in every sense but biological, and blesses his search for enlightenment. And it works!
K. Pinkerton Silverfish, the author of the titular self-help book in Stephen Manes' children's novella Be a Perfect Person in Just Three Days. The protagonist Milo does all sorts of ridiculous things at Dr. Silverfish's instruction, like wearing a stalk of broccoli around his neck, going without food for a whole day, and finally staying up all night doing nothing but laying in bed and drinking weak tea. When Milo screws up by nodding off during the last task, the book reassures him by explaining the moral of the story: nobody's perfect, and people who obsess over trying to be perfect just make themselves look silly.
In The Once and Future King the wizard Merlyn teaches Arthur/The Wart through a series of trials by transforming him into various animals to prepare him for life once he becomes the High King.
In Ender's Game, of course, the Battle School instructors have set up a system where almost everything the instructors do is part of a trick.
Master Li from Bridge of Birds (the namesake of the one under "Video Games") is a classic example. Being the son of two infamous bandits, he's partial to lengthy, intricate plots and bluffs in which Number Ten Ox is a part, and isn't afraid to put one over on his student from time to time, but he does manage to teach him effectively.
Live Action TV
Q, from the various Star Trek series, plays tricks that seem borderline evil at times, but ultimately contain an important lesson . . . unless he's just messing with you.
3 big ones, he engineers a contact between the Enterprise and the Borg, giving the Federation knowledge about them and time to prepare a year before they will arrive anyways. Another time, Q gives Picard a chance for a Do-Over when he was young and brash with the promise it won't affect others, leading Picard to discover that untidy past was necessary for him to be himself, and finally, Q sets up Picard to create the Paradox that would prevent life evolving on Earth; but at the same time gives him the tools to escape .
The Continuum itself managed a double-header. In making Q mortal for his constant jerk-ass behavior, they taught him a bit of humility, but also got to see how humanity would treat someone who had put them through so much aggravation while he was helpless.
The Trickster from Supernatural. Half the time he's teaching a lesson, and the other half he's just killing for fun. Oh, and he's anarchangel. Arguably, he is always teaching someone a lesson, these just usually go over the recipient's head. Often because said head is rolling away.
Claude from Heroes, whose training methods include gleefully whacking his pupil over the head with a stick and throwing him off the roof of a skyscraper.
Claude: "Do! Something! Unexpected!"
Mr. Roarke from Fantasy Island. He'll give you the means to fulfill your biggest dream, but it doesn't mean he'll grant said dream to you in exactly the way you want it to be. You'll have to learn your lesson through it, and sometimes your life and sanity will depend on it...
In their essay "The Sound of One House Clapping" (appearing in the volume House and Philosophy), Jeffrey C. Russ and Jeremy Barris argue that House is a trickster mentor in the classic Zen tradition. The closing arc of Season 3 has Foreman wrestling with the prospect that he's an Evil Mentor. This comes back in Season 6 after Chase murders a patient (an African dictator) to prevent him from perpetrating genocide on part of his country's population.
R.J. in Power Rangers Jungle Fury fulfills this role. He often will have the Rangers do seemingly stupid things in the name of teaching them valuable lessons.
Also Dimitria from Power Rangers Turbo, who spends much of her time speaking in riddles for the team to solve.
Slightly unusual use Chinese Paladin, as The Hero is this to his Lancer Jinyuan, setting him exercises such as standing on one leg and reciting nonsense. The twist comes when Jinyuan is perfectly aware that he's being set up, but goes along with it anyway—for the exact same reasons.
Trickster figures in myth and folklore tend to vary by region — particularly with the Native American tricksters. Raven was typically the more wise, trickster mentor. Crow tended to be more mercurial, even malicious. Coyote inhabited pretty much the entire spectrum between trickster creator, noble trickster, mean-spirited prankster, and avatar of chaos; depending on the particular region and people. African and European tricksters varied similarly by people and region. Anansi generally deviated between being brilliant but so lazy that he never got anything done and brilliant but so conceited that he stumbled over his own convoluted tricks.
Nasrudin (also called Nasruddin, Nasredin, and Nasreddin, or if you're an Arab, Juha, Jawha, Guha, and—deep breath—Goha) was the king of this. A famous Sufi Muslim form of this, he varies from eminently wise to incredibly stupid to a mixture of the two depending on the story. Besides being a general Trickster, he has a strong Trickster Mentor aspect. For example:
He was brought to hear the Emir (i.e. prince) recite a poem he had written. After all the other people in attendance had given their (very flattering) reviews, Goha (I'm an Arab) said: "With respect, my lord, your poem was terrible." The Emir immediately ordered him to be jailed for thirty days. Shortly after Goha was released, the Emir had another poem recital. When the Emir asked Goha his opinion, Goha immediately stood up and started for the door. "Where are you going?" asked the Emir. "To the jail, my lord," responded Goha.
Once a renown philosopher and moralist was traveling through the land and stopped in Nasrudin's village. He asked Nasrudin to recommend a place to eat, and, being hungry for intelligent company as well, invited Nasrudin to accompany him. At the restaurant, they asked the waiter what the special of the day was, and were told, "Fish — fresh fish!" They ordered two.
When the waiter brought the fish on a great platter, however, one was noticeably larger than the other. Nasrudin, seeing this, immediately slid the larger fish onto his own plate. The philosopher, shocked, proceeded to berate Nasrudin at length for violating the precepts of every religion and moral system ever thought of.
At the end of this, Nasrudin asked, "What would you have done?"
The philosopher said, "I, as a conscientious human, would have taken the smaller fish."
Nasrudin replied, "Here you go, then", and slid the smaller fish onto the philosopher's plate.
There are entire schools of Zen Buddhism and Sufi Islam dedicated to this.
Certain schools of Hinduism regard the Buddha as a Trickster Mentor of Hinduism: they believe that he was the ninth incarnation of Vishnu, sent to teach falsehood so that Hindus would know the danger of being sucked into reasonable-seeming but wrong religious arguments.
El Gallo in The Fantasticks is this, though the protagonists never quite recognize him as such.
Jade Empire furnishes a few examples. Master Li is characterized this way early on, with several characters remarking on his idiosyncratic behavior. The Forest Shadow is a more complete example: she's a powerful fox spirit (see the citation on Coyote above), a class of beings assigned by the Celestial Bureaucracy to confront humans with Secret Tests of Character—even when she needs your help, this is how she approaches you.
In Westwood Studio's 1997 game based on the film Blade Runner, Gaff acts as one to the protagonist Ray McCoy.
In Dragon Age II, Flemeth serves as one to Hawke. Despite the fact that everyone present is clearly aware that dealing with the "Witch of the Wilds" is a bad thing, she actually never does anything overtly malicious towards Hawke at all. Indeed, after Hawke honours their vow to bring her locket to the top of Sundermount, thus leading to her resurrection, she promptly thanks them for their help and even takes a moment to offer Hawke and their companions some cryptic advice before flying away.
Snarky!Hawke serves as one to Carver. Throughout the First Act, Hawke repeatedly tries to make their little brother get over himself and take himself a lot less seriously. Indeed, it seems that most of Hawke's jabs at Carver aren't those of mockery from an elder sibling, but more as means to try to push Carver to prove them wrong.
In Thog Infinitron, Shaman Magog acts both as Thog's mentor and trickster, often leading Thog into situations that will allow Thog to grow as a human being, but sometimes seemingly just for his own entertainment.
Netta from DDG veers between trickster or cynical mentor depending on her mood
In Ascension, Telious gives Aramis a sword and no training, and makes him face "zombie fight surprise" many times after it's very very clear Aramis has no sword talent or training. Then he sends Aramis (after having him fatally backstabbed by an assassin) against another zombie, but with no sword just a little golden whistle. Aramis technically fails the test by not even attempting to use magic for which he has no training, but passes it by attempting to kill Telious before he bleeds to death - and still keeping up the belief that despite Telious being a sick bastard he keeps hope because despair is a form of sloth his church warns against.
Not to mention Aramis is sent to scout ominous ancient evils that may or may not exist by himself, and not told the person he's supposed to meet is part demon yet a nice person! The total lack of instructions or even hints in dealing with evil makes this church's moral standards very peculiar indeed...
Dron the Dragon from A Magical Roommate, though not always in a good way- he tries to shake his students out of the 'learn what they tell you and don't think for yourself' mentality by forcing them to question everything and everyone, but fails to see that students need something reliable to trust, or they can't do anything.
In Whateley Universe, Chou is 'blessed' with the Monkey King as a mentor. In "Summoning Sweeties", the Monkey King explains his/her actions all but quoting this trope.
Rafiki the baboon from The Lion King. Behaves like this only during Simba's revelation that he cannot keeping moping over his past, and returns to his homeland to correct the Circle of Life (he actually whacks Simba over the head with his staff, without warning). However, he may act like this more often, outside of the story.
Iroh arguably also fits the mold, though his ward turns out to be so thickheaded that eventually he just ends up spelling out his teachings when the subtleties fail.
The Oracle of Delphius from Sonic Underground fills this trope. He comes complete with koan-slinging and a lampshade.
Manic: Do you ever give a straight answer?
Oracle: What do you think?
Princess Celestia from My Little Pony: Friendship Is Magic. She so often sets up the episode's whole source of conflict, runs away when anything dangerous happens, or chooses not to be a Deus ex Machina even when she could easily solve everything on her own that fans have dubbed her "Princess Trollestia"
In the series premiere, she knows full well about the prophecy predicting that her sister whom she imprisoned is about to escape and wreak havok. Rather than explain things, or even do anything herself, she just tells the protagonist to "stop reading those dusty old books" and make friends, and is absent for the rest of the episode. Incidentally this is exactly what needs to be done, and as she notes later, she never explicitly said that the prophecies were wrong.
She knows that Twilight has six friends, but gives her only two tickets to the Gala, forcing her to agonize over who to give the extra ticket to. Though there is some controversy over whether she might have honestly expected Twilight to just go with Spike. In the end Twilight returns the tickets saying she can't go if she can't bring all her friends. Celestia replies, "Why didn't you say so in the first place?" and gives her more tickets. Apparently the lesson was: You never had to choose.
She sits back and watches as Rarity plummets to her doom, letting Rainbow Dash have a Big Damn Heroes moment. The fact that Rarity was put in this situation due to the heat of the sun, and the fact that Celestia controls the sun, leads some to suspect that she caused the whole incident to begin with.
She invites the main characters to a snooty, boring, rich-people party and hopes that they'll cause a disaster and liven up the event. She outright admits as much after said scheme goes precisely as she planned.
She intentionally tricks overzealous waiters into filling her teacup so that it overflows. This is an undeniably harmless joke, though, and seems to have been made as an attempt to break the tension her presence caused her overly nervous subjects. Though she still clearly enjoys it.
She takes her old, dying pet bird to a party, then runs away and leaves it there with Fluttershy, resident animal lover, failing to tell her the bird is actually a phoenix whose time for rebirth has nearly come. Again, the debate as to whether this was purposefully done or simply a case of absentmindedness continues.
She seems remarkably nonchalant when she discovers that Twilight has traveled all the way to Canterlot and broken into the Canterlot Library of Magic's Star Swirl the Bearded Wing at the crack of dawn - all while sporting a torn jumpsuit, a wildly unkempt mane, a scar on her cheek, and an eyepatch. Almost as if she suspected what was going on but didn't want to interfere with Twilight learning a valuable lesson...
She sends Twilight a valuable uncompleted spell from one of the mages of all time, in hope that Twilight could fix it, suggesting that she knew very well what was wrong with it...and doesn't bother giving her a heads-up that it completely changes the destiny and lives of all her friends. Her justification was that by saving her friends and completing the spell, she was ascend to become an alicorn princess, too.
Subverted with Magic Man in Adventure Time. He pretends to be an old homeless man and begs Finn for food, and then does Finn "a favor" in return: transforming him into a giant foot. He claims that he did so to teach Finn a lesson; and only changes him back when Finn expresses regret of having given Magic Man the food. No one can figure out the lesson in the end.