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 of Naruto. 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.
Not to mention that 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. Not to mention, 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. Of course, 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.
That barely scrapes the surface of how whacked he is. 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 the hell 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 is fairly handsome, being a White-Haired Pretty Boy and all that, but damn did he have a rough life. To recap: father died before he was born and his mother died when he was only a few years old, making him an orphan at a young age; he is a half-demon, which has caused him to be ostracized by both human and demonic society, including his older full-demon brother, the only remaining family he has left; the first girl he fell in love with was brutally murdered and he was framed for the crime, with the girlfriend binding him to a tree, declaring her hatred of him in her last moments alive. Small surprise he has an abrasive personality.
Most major characters from Evangelion qualify as Troubled But Cute to some extent.
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. Teito also qualifies.
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 even 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. Still stubborn as hell, 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, she's in junior high, and she doesn't use leather. But boy, ain't she makes up for this with an extremely troubled past. Originally, though, she was Adorkable.
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 from Empowered, period. The trouble's in the name, and the leather jacket is also included.
Ninjette and Spooky are rare female examples of this trope. 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. As for Spooky, 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).Despite this, both girls are both adorable and way tougher than your average Broken Bird, and both can pretty much kick an entire army's butt single-handedly.
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.
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.
This trope is 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.
However, as we learn later, he is more in the line of "he doesn't deny any of this, so it must be true". He does stay away from most of his peers, but that's mostly because he just does have different tastes. Kate is the real Troubled, but Cute, with her open disgust of the people around her and even with her "the reason I am so angry at everyone" backstory.
Billy Tallent and Joe Dick of Hard Core Logo are what happens when examples of this trope hit their thirties, with emphasis on the "troubled" part (especially in Joe's case).
Kovu from The Lion King 2 definitely fits this trope - if he wasn't, you know, a lion, he would definitely wear leather jackets and ride a motorcycle.
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.
Rafael Gives Light, from the Gives Light trilogy, a loner who is known for getting into fights at school and, oh yeah, 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.
Sawyer from LOST is this backwards and forwards. Eventually, Jack catches up to him, though he loses some of his cuteness by crying all the time (sorry Jack-fans, but you know it's true).
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!
You forgot to mention creepy moms, being ridiculed by your peers while alive, and, later, guilt for the "troubled" part. And low social skills for the "cute" one.
Some might argue that Dr. Cox from Scrubs is an example of this. 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.
Both The Todd and Turk have been shown as regularly working out at the hospital. That said, Cox is rather studly.
Adding to both the troubled and cute (or at least honorable) is Cox's violent temper over being a perfectionist. The cute/honorable part is that his perfectionism is over saving his patients' lives.
Jess on Gilmore Girls, who never actually got around to having a heart of gold.
Jess 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. Ugh.
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, not to mention the unexpected vulnerable streak.
Dean from Supernatural, and it didn't take long for his brother Sam to catch up. Castiel also fell into this before too long, further proving that improbably good-looking men angsting a lot is kind of the show's main draw.
Shawn Hunter in Boy Meets World. The rampart trailer park trash jokes started as innocent and one dimensional character traits. Then, for a good while from season two onward, it seemed like every other episode was a Shawn pity-party fest. And he got girls to boot.
Tyler counts as well, as does Vicki as the female equivalent.
Oscar Cole of MI High is this, although his dad eventually came back and his mum was put into prison for good, so life got better from there.
Some early episodes of Happy Days show Fonzie coaching the boys on how to act this way in order to arouse female interest.
Willa from The Finder is often in trouble with the law but is shown to have a softer side.
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.
Renee: Ugh, you're so stubborn... I kinda like that.
Tony: Now's not the time for that!
The protagonist from Jak and Daxter becomes this as of the second game. You know, after all the Dark Eco experimentation.
Mass Effect presents FemShep's potential male love interests, in order of least-to-most emotional baggage: Jacob (refuses to be thought of as a "baggage guy") -> Kaidan (Training from Hell, Blessed with Suck) -> Garrus (Cowboy Cop with a lot of survivor guilt come the second game) -> Thane (former assassin who made his first kill when he was twelve). Now, where Liara would fit on this scale is another question...
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.
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.
Roger Klotz in Doug. He and Doug even get along once in a while, to show that he's not just a horrible jerk.
He's also somewhat of a woobie. Sometimes, his mom doesn't spend a lot of time with him, and his dad lives in the next town over (his parents are divorced), AND lives in a trailer park (in the Nickelodeon version). Kinda makes you wonder why he started bullying in the first place.
In one episode of Birdz, we meet Riley Raven, a good-looking bad boy who does pretty much 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 fangirls.
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.
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."