Kujira Kurokami from Medaka Box based her life on the saying, "Something amazing can only be made after seeing hell," believing that any happiness would keep her from creating her best work. Thus, she forced this trope on herself, even going so far as to run away from her well-off family, change her name, hide her face, and erase her memory.
Though it isn't explicitly stated, a large portion of the backstory of Berserk goes into showing why Guts is such a hardened (and therefore exceptional) warrior. Most of his life has been misery heaped on tragedy, forging him into an inhumanly durable person.
On the other hand Casca most definitely did NOT become stronger from her misery. After all, this trope only works when applied moderately, not in excessive doses.
Dark Magical Girl Fate Testarossa became the kindest and easily the most heroic character of Lyrical Nanoha series because she was abused and abandoned as a child, resolving to let no more children share her fate on her watch.
"You live a life like mine, you end up with a pocketful of regrets. A good regret gives a man character, if you ask me. I didn't get to be this handsome and laconic through clean living."
In the Intimates, Punchy stops Dead Kid Fred from committing suicide. Later, it's revealed that he wished he hadn't gotten to him in time, because having a death on his conscience like that would've made people take him more seriously as a hero - would have made him a better hero. This may have something to do with the fact that the murder of his sister sparked his career as a superhero to begin with.
Duke more or less exhibits the trend, as well, being probably the nicest of the main characters while having probably the worst home life.
This was the rationale of The Flash villain Zoom, who attempted to murder Wally West's wife, believing that West needed to suffer personal tragedy in order to become a better hero.
Over the course of Art Spiegelman's Maus, Spiegelman's father Vladek states several times that, although his time in the concentration camps was horrific beyond measure, he learned several skills that would serve him well later in his life.
"Some believed that we lacked the programming language to design your 'perfect world,' but I believe that human beings as a species define their existence through misery and suffering."
Literature
In Robert Jordan's Wheel of Time series, White Tower initiates suffer this trope. They must do all their chores by hand, without using their mystical powers, because menial labor is misery that builds character.
Black Tower trainees invert both the trope and the above example. They must use their mystic powers for everything, including lighting lamps and cooking dinner— so when they first start their lessons, they find themselves eating raw food in the dark. This is misery too, but the instructors couldn't care less about "character." They're just motivating the students to practice.
Fridge Brilliance : from the moment a man touches Saiden, he has only a limited amount of time before madness and death claims him. He has to learn everything he can as fast as he can. Tick tock, Asha'man, tick tock.
This is implied in Harry Potter; growing up with his abusive Aunt and Uncle gave him a lot more humility than his father had at the same age (although his father grew out his Jerk Jock phase eventually). This is contrasted with Voldemort, who hated the orphanage he grew up in, but was responsible for making it an Orphanage of Fear.
Appears frequently in stories about British childhoods (especially holidays before mass air travel), such as Emma Kennedy's The Tent, the Bucket and Me about her family's disastrous camping holidays in the '70s.
A recurring theme in Tall Tale America is that people can only get to be heroes if they've got plenty of "rock-ribbed harships" to overcome. Heck, Pecos Bill intentionally makes the cowboy business extraordinarily difficult, just so the cowboys who manage to survive it will be the best there ever was.
In the Quantum Gravity series, devils plant themselves on a victim and whisper these kind of thoughts, keeping the victim in Hell*
read as "separation from God"
. Demons get...touchy if you confuse demons and devils, as demons believe the exact opposite. Have fun at everything you do, be it painting, singing, fighting, killing, decorating, what have you. A demon with a devil on it isn't even considered a demon anymore, it's an imp.
Crabbit in the Magic Kingdom of Landover series appears to espouse this view. And judging by Mistaya's Character Development while at Libiris, he may be right.
Vergere does this to Jacen BIG time in NJO's Traitor.
Subverted in the Star Trek: The Next Generation episode "New Ground," when Worf tells his son Alexander that the rigors of Klingon schools are meant to build character — but that their staying together will be an even greater challenge.
The series finale of Malcolm in the Middle has Lois sabotage Malcolm's chance at a high paying job because she believes he needs at least a decade more of suffering before he's ready to pursue what (she believes) is his destiny: to become the best President of the United States ever.
Unfortunately, it also leads to potentially bad consequences since most of the suffering the family endured was inflicted upon themselves, and they want Malcolm to essentially carry the burden of their selfish, self-destructive behavior.
Ace Rimmer from Red Dwarf is this all over. He is different to normal Rimmer because their shared timeline split off when they were children. One of them got held back a year in school, the other didn't. It turns out it's actually Ace that was held back a year, and so he suffered for it (ie by being bullied and suffering the humilation of it all), and decided to fight back, and continued to fight back ever since, building his character and becoming awesome. Normal Rimmer, on the over hand, was never held back a year, and therefore spent the rest of his life making excuses for himself.
According to Red on That '70s Show, "In order for [my son] to be a responsible adult, he has to be miserable now!"
Newspaper Comics
As the trope quote shows, Calvin's dad would often invoke this phrase whenever Calvin (or his mom) complained about their current activity. Bill Watterson stated in the tenth-anniversary book that he took this trait directly from his own father.
It's also a crowning moment of funny for his mom considering how she cracks up afterwards.
Calvin's Dad: Okay, the voice was kinda funny, but that's one darn sarcastic kid we're raising.
At one point Charlie Brown declares that he already has enough character, thank you very much.
In another Lucy assures him, "We learn from our mistakes," and he bellows plaintively, "THAT MAKES ME THE SMARTEST PERSON IN THE WORLD!"
At one point, after Snoopy's doghouse burned down rather tragically, Charlie Brown went to Lucy's booth for some counseling on why these tragedies occurred, to which she gave the rather philosophically pat answer that adversity helps prepare us for what lies ahead in life. For what are we being prepared, then? "More adversity. Five cents, please."
Tabletop Games
Champions adventure Deathstroke. The title villain group decided to make their agents monitor the base's surveillance cameras instead of letting a computer do it because they felt that the boring duty would "build character".
Theatre
"Money Isn't Everything" from the Rodgers And Hammerstein musical Allegro sarcastically lists the deficiencies of money, concluding that "it cannot build your character or teach you how to starve."
Video Games
Team Fortress 2 - The Soldier believes this, according to one of his voice clips: "Pain is weakness leaving the body!"
Webcomics
MAG ISA — This is the whole point of this comic. Eman, the main hero goes through a lot of misery that the average person would probably end up just killing himself/herself.
In thisUser Friendly strip, Sid claims that obsessive addiction to Nethack is a good thing because it helps build character.
"...[B]ein' a dwarf is about doin' yer duty, even if it makes ye miserable. ESPECIALLY if it makes ye miserable!"
Western Animation
After the Eds wrongfully accuse Jonny of being a "serial toucher" and sentence him to rolling down a hill in a giant tire, Eddy justifies it by citing the trope.
And given his rather shocking history of abuse from his brother, he might just believe it.
Zuko: I don't need luck though, I don't want it. I've always had to struggle and fight and that's made me strong. Its made me who I am.
Of course, he's just trying to please his Magnificent Bastard father, who claims this is the case, but his philosophy is actually Might Makes Right. His son doesn't agree? Teach him a permanent lesson... On his face.
Ozai: You will learn respect, and suffering will be your teacher.
Zuko: ''How can you possibly justify a duel with a child?'
Ozai: It was to teach you respect!
Zuko: It was cruel! And it was wrong!
Batman is always described as pretty much the very essence of this Trope. The loss of his parents made the (probably) most strong-willed person in the DC/DCAU-universe.
In the House of Mouse episode "Goofy For A Day" Max decides to be a waiter to prove to Goofy that waiting is an easy job. When it proves to be tough for Max, Goofy tells him that "goofing up builds character".
Real Life
Truth in Television in that there are people who subscribe to the philosophy, but sadly, not the desired effect. Bully apologists, for example, use this as an excuse to sit idly by and allow bullying to continue, believing that the abuse will make the victims stronger. The results: not so much. While it is true that people have become stronger in the face of adversity, this does not mean adversity always makes someone stronger.
This does seem to be justifiable Truth in Television when applied to media creators making their characters miserable. Tortured characters seem to sell very well, as long as it doesn't veer into Wangst or Deus Angst Machina.
And plenty of people who've experienced hardship (of any magnitude) value having had the experience because it taught them some sort of useful skill or helped them grow as a person, though they generally agree that they wouldn't want to do it again.
YMMV on whether or not this is actually required to function to an extent. However there is a limit (you may get PTSD for example, which is more a breaking of ones character rather then development of it).
The flip-side being is that, since everyone's life always has its hardships, there's really no reason to go piling them on simply for extra misery.