Harima Kenji from the anime School Rumble takes a lot from this trope. Being rather antisocial and a juvenile delinquent, with a liking for leather jackets and bikes, he likes beating up Yakuza goons and is all around good-looking...except that, beneath all that, he's an oaf with a heart of gold who likes drawing manga and is too scared of confessing his love for a classmate. All while obliviously gaining the attention of several other girls.
Sasuke completely misses the look (or at least, the dress code), though - that turtleneck, shorts, and kneesocks combination fairly scream "scrawny kid". Then again, Ninja are supposed to cultivate an unassuming personal appearance, even if, in fiction, they usually don't. He gets...better when he gets an Akatsuki trench coat and a Kill 'em All attitude later on.
Fakir from Princess Tutu. He even has a fanclub at his school, although it's likely none of his fangirls have ever talked to him, given his anti-social nature.
Kyo Sohma from Fruits Basket, an antisocial martial artist with Don't You Dare Pity Me! attitude who's obsessed with beating Yuki. Tohru seems to genuinely like him, though, and in his defense, he does have a good Freudian Excuse: his mother was Driven to Suicide, his father rejected him completely after that, and being the cat of the Sohma clan has brought him lots of unhappiness, Akito's scorn, and an uncertain future.. His reason for obsessively trying to beat Yuki doesn't make him a bad guy at all: Akito said that if he beat Yuki fairly (at anything), he won't be locked in isolation until he's dead. His general issues with Tohru are revealed at the very end of the manga to be the result of how he could have stopped her mother Kyoko from being hit by the car, but grabbing her would have caused him to transform into a cat. He blamed himself for being a coward (a running theme in his Character Development) and thought her dying words were her blaming him and telling him to stay away from Tohru (in reality, Kyoko was trying to ask him to protect Tohru, but she was dying at that moment and couldn't finish).
Sagara Sousuke from Full Metal Panic!. Although he's not "troubled" in the normal rebellious sense, and more just plain troubled. It's pretty obvious that the poor boy has Post Traumatic Stress Disorder and an automatically violent personality that he can't control. His extreme paranoia has him doing things like bombing his school, planting land mines everywhere, and pointing guns/shooting at people. All of this is played for laughs, and he tends not to angst (considering his past and current situation, he angsts remarkably little). And despite all this, any girl (or guy, even) who has watched him or gotten to know him well enough seems to fall for him - even the series' resident Tsundere. On one occasion, Kaname was kidnapped by a group of thugs who planned to back him into a corner. He retaliated in a way so nightmarish that, that particular episode wasn't aired for a while because of a similar incident in real life. Then, when she got kidnapped AGAIN by the Yakuza, Sousuke went after her with a rival gang clad in theme park mascot suits converted into powered armors. Seriously, who would convert theme park mascots into powered armor and try to sell it to the military and law enforcement sector, then wonder why didn't it sell? He first stole the suit while trying to keep an eye on Kaname while she was at an amusement park and decided to make it more useful in the future by upgrading it. He's dumbfounded by it not selling because his raised-by-wolves attitude left him without a sense of aesthetics, so he didn't realize just how silly it looked.
Ciel Phantomhive from Black Butler is a Hollywood Atheist in Victorian England. Check that page for his Freudian Excuse, if you don't know his backstory already. The result is a stubborn, bitter teenager who honestly believes that once something is lost, you can't get it back (a plot point in the anime) and has a serious issue with showing his real emotions unless it's anger. Despite this, there are still girls (and two or three men) in universe who like to fawn over him, and aside from Sebastian, he has an extremely large fanbase out of universe.
InuYasha: Inuyasha is considered cute (especially his ears!) but had a very rough life. His parents died when he was young, leaving him with only a few memories of both of them* The third film changes this to his father dying on the day he was born and his mother dying when he's an older, but still pre-teen, child. As a Half-Human Hybrid he is ostracised by both human and youkai societies. Even his older brother mocked or ignored him when he was growing up, escalating into Sibling Rivalry and a temporary bout of Cain and Abel when they both discovered Inuyasha had inherited their father's famous Infinity+1 Sword. He was torn apart from his First Love by the Big Bad who framed them both, causing them to turn on each other in anger and hatred in the moments before she was brutally murdered and he was sealed to a tree for fifty years. Only after he meets Kagome, Miroku and Sango does his life begin to improve for the better. Eventually, he even makes peace with his brother.
Bishop Frau in 07 Ghost. Badass badboy who disregards convention and does as he pleases. Still, he has a difficult backstory and is a genuinely caring person.
Mikael from Tenshi Ni Narumon is a very, VERY troubled and unstable pretty boy. You wouldn't guess that because for the first 13 episodes, he acts very little, and when he does, he's usually calm, polite, always smiling gently - an epitomy of sanity in a crapsack world. Then, in the second season, we get to see the real him under that mask - a very stubborn, obsessive, and insecure boy. And at the end, he goes all evil and insane and has an epic breakdown - and then he returns back to his former self. He remains stubborn, unfortunately.
Akemi Homura from Puella Magi Madoka Magica has the same vibe as most characters on this page, with a few exceptions: she's a girl and she's in junior high. But boy, doesn't she make up for this with an extremely troubled past.
Chapter 36.5 of Natsume Yuujinchou shows that Natsume, of all people, had a reputation as the pretty-but-seriously-disturbed boy back in middle school. That sort of thing happens when you're regularly attacked by things almost no one else can see.
ThugBoy. The trouble's in the name, and the leather jacket is also included.
Ninjette is alcoholic and on the run from her abusive, psychopathic father, who fully intends to amputate her limbs and use her as a breeding machine. Despite this, she is adorable and way tougher than your average Broken Bird, and she can kick an army's butt single-handedly.
Spooky (female example), even before she had a breakdown as the result of her girlfriend dying horribly, Spooky has paralyzing self-esteem and bullying issues (and seems to lack a family, despite being high school age). She is cute and tough as nails (She's able to kick an army on her own).
X-23. Troubled is an understatement. She was created to be a living weapon, tried to rebel against her training, ended up as a teenage prostitute, and then, after joining Xavier's School, ended up conscripted to X-Force, a squad created specifically to kill people that Cyclops deemed a threat to mutantkind, which has alienated many of her very few friends. The books make it very clear that Laura is a very beautiful young woman: several characters have outright called her hot, when planning to pull a Grand Theft Me on her Miss Sinister expressed satisfaction she would be getting a very attractive new body, and she caught the attention of both pretty boy Hellion, and the time-displaced teenaged Cyclops (and this despite being on a team with the teenaged Jean Grey).
Spider-Man. Brilliant, athletic (in secret most of the time), magnet for beautiful women of all hairstyles... and yet he's haunted by death, failure and the worst luck in Marvel Comics.
Chase is a cute bad boy who's still haunted by the death of his girlfriend and for a long time believed that he'd killed his own uncle.
Victor Mancha is a Long-Haired Pretty Boy who's also the son of a genocidal robot, and may be fated to become an Omnicidal Maniac. In one alternate future, he's also the only surviving Runaway after his evil dad went on a rampage.
Klara Prast is an adorable plant controller with unaddressed psychological issues stemming from sexual abuse. She also still believes that she's responsible for the apparent death of the team's beloved pet deinonychus.
Tommy from Warrior. He's ridiculously damaged, and has got a fractured (to the extreme) relationship with his father and his brother. But he's a good guy, as shown by his reason for entering the tournament and by how he selflessly saved a bunch of marines in the war.
Dan from Peaceful Warrior. Bitter, arrogant and anti-social, especially after his leg is severely injured in a motorcycle accident. Nonetheless, he's very handsome and athletic, and manages to attract the attention of Joy
Roger Davis from Rent. The guy has HIV and is really, really cranky, but is still beloved by any straight girl.
This trope is Discussed and mocked through Zeke in Disney Channel's movie Minutemen, when girls come up to him and ask, "You know, you're kind of scary and unapproachable... can we sit with you?"
Fans of Repo! The Genetic Opera are divided over whether or not Grave-Robber is actually troubled or just a sociopath with a sense of humour, but there's no denying he's incredibly foxy. The fact that he canonically lives out of dumpsters seems like it would be enough to make him the former.
Kovu from The Lion King II: Simba's Pride definitely fits this trope - if he wasn't, you know, a lion, he would definitely wear leather jackets and ride a motorcycle. he has dark charms and mysterious vibes and Princess Kiara likes him immediately. His family makes his life difficult and miserable because they supported Scar, Simba's (Kiara's father) arch-enemy.
Luke from Cherrybomb. One the one hand, he's a violent, arrogant drug-dealer who treats his best friend like crap. On the other, he's a lonely, angel-faced◊ sixteen-year-old boy whose father abused and abandoned him.
Audie Murphy had a number of Troubled, but Cute roles early on in his career, including his portrayal of Jesse James in the bland and highly inaccurate Kansas Raiders. Universal stopped putting him in these roles once they realized that his fans preferred him in Beware the Nice Ones mode.
Sirius Black in Harry Potter, though, rather than being antisocial, he is represented as popular, despite various acts of callous teen cruelty. At least, as an adult, he is a good person at heart. Judging from his possessions, before the Potters got slaughtered by Voldemort, he was a biker.
Turin Turambar from Children of Hurin and Aragorn from The Lord of the Rings are both described at points as being handsome but grim, though Aragorn downplays both the handsomeness and grimness in comparison to Turin.
Nico di Angelo from Percy Jackson and the Olympians. Emphasis on the "cute", since he's only twelve years old, but he's certainly troubled after his sister's death. Taken to a whole new level in The Heroes of Olympus after he's been through Tartarus, literally and we find out that he used to have a crush on Percy that he couldn't deal with, causing him to avoid other demigods.
Yozo Oba of No Longer Human, who is always depressed and fears other people, cannot help but attract women throughout his life due to his apparent good looks.
Rafael Gives Light, from the Gives Light trilogy, a loner who is known for getting into fights at school and his dad's a serial killer. Only the main character ever describes him as attractive however, and only after he's already falling in love with him.
The Changeover: Sorenson 'Sorry' Carlisle, something of a subversion in that his troubled side doesn't show when he's in public, rather he holds up a facade of a polite, well-behaved young man. Was abused as a child, and suffers from an inability to emotionally express himself, or connect with others, as well as somewhat sinister behavior towards the main character near the beginning of the story.
Spike and Angel from Buffy the Vampire Slayer and later spinoff Angel. Bad boys. Leather coats. Troubled by their love for a pretty slayer. Hearts (well, souls) of gold! Creepy mom (in Spike's case), being ridiculed while alive, and, later, guilt for the "troubled" part. Low social skills for the "cute" one.
Scrubs: Dr. Cox. Troubled? He perpetually sees a shrink, regularly abuses the people he cares about, and is in love with a woman that he hates. Cute? He appears to be the only doctor in the place that regularly exercises. Plus, he's very proud of being forty and retaining all of his hair. Cox's violent temper wins over him being a perfectionist. The cute/honorable part is that his perfectionism is over saving his patients' lives.
Most of Claire's love interests on Six Feet Under. She was dark in a way, but beautiful, kind and caring and a magnet for all the troubled boys. Her mother lampshades it by saying that she's an angel, so naturally, they are attracted to her and want to be "saved" and redeemed. However, the real question was why Caire felt compelled to start a relationship with them, knowing how messy it would be.
Gabriel was Claire's high school boyfriend with certain charms and jerk vibes. He wore dark clothes and jeans, and he had tattoos and piercings. Gabe gave her strong drugs and told everybody about their sex experience (she sucked his toes, which made her a laughing stock). His family background was horrible: a white trash mother, a father who abandoned them, a jerk of a step-father, and he had to deal with a death of his small brother. He later got suicidal and then committed burglaries. He got lost later, and Claire sort of learnt about his fate when she might or might not have visited afterlife.
Claire dated Russell in college. He was very insecure and possibly gay or bisexual who was uncomfortably with his sexuality. She told him he was hot, but he said the best he would get was cute, considering it Damned by Faint Praise. He's a talented artist, though, and attractive enough to be sought out by their male professor who had sex with him while he and Claire were dating.
Brenda's brother Billy once used Claire when she was a teenager, trying to get to close to Brenda and Claire's bother Nate. He had a weird relationship with Brenda, verging on brother-sister incest, and his parents screwed them both up horribly, over-analyzing them constantly. They had some happy moments, but once bipolar Billy decided to stop his medication, it went to poop.
Gregory House of House, both in-universe women seem to adore him unless he does show his Dr. Jerk tendencies. He has lots of emotional baggage from his past relationships, abusive father, and his chronic pain in leg. He is played by Hugh Laurie who is Tall, Dark and Handsome with deep blue eyes and sense of humour.
Jess on Gilmore Girls, who never actually got around to having a heart of gold. He got to heart of bronze-silver alloy, but it's a rather subtle thing. He probably would have gotten the heart of gold if they hadn't put him on a bus to California to live with his biological father in order to set up a spinoff that never happened, and moreover, his heart of gold got to shine later in when he reappeared for two episodes in the sixth season, having grown out of his jerkiness and into some responsibility (paying Luke back for at least the car and NOT making out with Rory when she reveals she's still with Logan).
Christian Troy on Nip/Tuck. He's shallow, sex-obsessed, and in the habit of treating his sex partners like dirt — but he's also handsome, successful, and really good in bed, plus the unexpected vulnerable streak.
Daniel Desario from Freaks and Geeks is a James Dean-looking, scholasticly-challenged heart breaker from the wrong side of the tracks, yet manages to have both female leads wanting him
Neal Caffrey of White Collar. Troubled is a given, considering he's a con artist and everything, and cute... well, just look at those eyes.
Played for laughs with Bud Bundy from Married... with Children. He tries to create different troubled but cute persona's to get young women, like his infamous Grand Master B character. The funny thing is, it mostly works until one of the family members interrupt and reveal his true character.
The former is a traumatized survivor of a shipwreck that left him stranded on an island; he's self loathing, has lost most of his former social skills, and is plagued by guilt, both survivors guilt and guilt for hurting his ex girlfriend, who he's still in love with. He's also an in-universe Memetic Sex God of sorts.
Roy Harper is a brooding orphan who's spent his life fighting to survive poverty and looking out for himself, is a petty crook that most write off as a thug, and like Oliver he's a self-loathing bag of guilt with no social skills who always looks out to help others when he can.
Eli "Weevil" Navarro for a straighter "Bad Ass leather-clad biker from the wrong side of the tracks who is kinder than he lets on" example.
Jeff from Community. Has attracted the attention of every female main character, as well as several one shot girls and a few guys, but he's narcissistic, moody, has anger issues, a drinking problem and when it comes down to it is a severely depressed broken man.
Renee: Ugh, you're so stubborn... I kinda like that.
Tony: Now's not the time for that!
Both non-DLC male Love Interests in Dragon Age II, lampshaded on occasion by Varric. The girls count to a lesser extent as well, particularly Merrill. It's just the boys who get the "brooding" jokes (especially Fenris).
Zelos Wilder from Tales of Symphonia: he's a young, playful womanizer with long, red hair, flirting with every woman and having a bunch of Fangirls (his "Hunnies"). But later in the game, it is revealed that he never had any real parents, his father was absent due to his forced marriage to Zelos' mother, who states that he "should never have been born". This made him develop a great self-loathing and the feeling of worthlessness. In the superficial society of Meltokio, he was forced to lock his emotions away, therefore adapting to their expectations. This made him becoming the playful, careless guy he pretends to be.
Solid Snake is considered by the women and men of his universe to be extremely attractive and glamorous (at least, before he gets old), but has a history involving drinking problems, mental illness, emotional isolation, and murder, as well as being difficult to handle and having a moody personality. However, another character tells him, "That's what I like about you. That's what makes you human."
Big Boss is an Even the Guys Want Him character, known for his charisma, presence, and magnanimity, who has had romantic and pseudo-romantic relationships with both women and men. He killed his mentor, and spends the rest of his life attempting to come to terms with it and trying to stick it to The Man...who turns out to be an actual character (his former best friend!)
Raiden at first comes across as well-adjusted, but turns out to have been a recovering ex-child soldier with messed-up standards of intimacy. But...so bishie!
Norman Jayden from Heavy Rain is quite handsome, but spends most of the game struggling with a debilitating addiction to triptocaine and his overuse of the ARI. Things get even less pretty when he starts having withdrawal symptoms from trying to break himself out of the habit.
Miguel Caballero Rojo in Tekken 6 is the black sheep of his family who keeps on picking fights, arguing mostly with his parents, and running away from home at an early age. But in all this, he has a soft spot for his sister.
Inui Arihiko in Tsukihime, until Shiki stole all his luck with girls away, which made him a little bitter. In-story, Shiki himself might actually count, despite practically being a paragon of virtue. However, he actually tends to scare people due to familiarity and closeness to death. Yet the same people find themselves falling in love with him (Satsuki, Arcueid, Akiha, etc.) regardless.
The Autobiography of Jane Eyre: Mr Rochester is out of the preferred young teenage phase, being about thirty in this Setting Update. Otherwise he fits perfectly: a pair of jeans, a leather jacket, tattoos, and Perma Stubble. He can be extremely harsh or even rude to Jane, but he's still attractive and fangirls have been swooning over him since he first appeared. The creators teased their viewers with the constant Unreveal, but the wait was worth it.
Subverted in Kim Possible: Ron tries to become this character to get a date. It doesn't work, and through a little accidental Applied Phlebotinum, he becomes a full-on supervillain.
Zuko. A leather jacket wouldn't fit the medieval Asian "look" of the show, so he makes up for it with a facial scar linked to his tragic Back Story.
Mako from The Legend of Korra. Growing up on the streets while simultaneously raising your little brother will make even the hottest firebender stoic and brooding.
In one episode of Birdz, we meet Riley Raven, a good-looking bad boy who does whatever he wants, and is considered a "bad egg" for it. We later learn that he acts this way because of his workaholic parents never having time for him.
Batman, as epitomized here in Justice League, where he's trying to convince Wonder Woman why they they wouldn't be good together:
Batman: "You're a princess from a society of immortal warriors. I'm a rich kid with issues. Lots of issues."
In one episode of The Simpsons, Millhouse temporarily became one of these, complete with anti-socialness, a leather jacket, and in-universe fangirls. Even Lisa found that attractive
Terry McGinnis in Batman Beyond seems to be Troubled, but Cute in the first couple of episodes before he opens up and reveals that he's actually a responsible, altruistic young man. He was a straight example in his Back Story, which included a stint in juvie.
Lance Alvers, aka Avalanche, post-Characterization Marches On. At first he was just a straight up criminal, then he gained some Noble Demon aspects and a soft spot for the Kitty of the X-men.
Gambit is handsome and charming, able to leave people paralyzed via them being Distracted by the Sexy, and a criminal who grew up being used by his adopted father and hunted by the rival gang.
Evan Daniels. Scruffy athletic teen rebel with a penchant for trouble, but, even after his secondary mutation, is still not exactly ugly.
Johnny 13 of Danny Phantom, complete with rebel bike and all. He already has a girlfriend whom he loves despite his flirtatious nature and her constant nagging to keep his eyes focused on her at all times.
The characterisation of Jim Hawkins in the original Treasure Island mostly revolved around his maturation to a man who knows the meaning of honour and duty and can be held responsible for his actions. The Disney adaptation of Treasure Planet Woobiefied him by making him more of a troubled troublemaker trying to find his place in the world, with low self-worth and paternal abandonment issues.
The front men of the other big four grunge bands (Layne Staley of Alice In Chains, Eddie Vedder of Pearl Jam, and Chris Cornell of Soundgarden, respectively) as well.
Melanie Lynskey is cute as a bug's ear, but tends to play characters that are, to say the least, quirky.
John Lennon was a drug addict, had a quick and fiery temper, and generally could be a downright Jerk Ass a lot of the time; but being a Beatle, he had no shortage of screaming fans, and Paul Mc Cartney has been quoted as saying of those who actually KNEW John, "Everyone was in love with John; John was lovable, John was a very lovable guy."