Benedict Cumberbatch's portrayal of the young Stephen Hawking in Hawking is a mild example. He does show positive emotions at times - enthusiasm for science and affection for his girlfriend - and is Adorkable then, but throughout most of the film he's quite stoic about the fact that he's been diagnosed with a degenerative neurological illness and may not live to complete his doctorate. This arguably makes the few moments he does break down all the more heartbreaking.
Gibbs and Ziva from NCIS. Gibbs, who is the resident stoic, lost his wife and eight-year-old daughter to a drive by shooting. Ziva was held captive by terrorists, tortured, and who knows what else for four months between seasons 6 and 7. As of the tenth season, she has lost her entire family - mother, father, younger sister, older brother - and yet whenever anyone asks her how she's doing, she always insists that she's fine.
19-2: Through all his travails, Ben is wrapped tighter than...well, extremely tightly. Which makes the few glimpses of emotion he lets escape more powerful.
The original "Behind Blue Eyes" by The Who is a textbook example. Not to be confused with Limp Bizkit's infamous cover version, which is a prime example of gratuitous Wangst, instead.
Anyone with Aww! XP in Chuubo's Marvelous Wish-Granting Engine. The standout would be the Prodigy from The Glass-Maker's Dragon, an icily emotionless usually-Russian badass who, deep down, believes Hope Is Scary because the last time she hoped, she lost a loved one or had another traumatic experience.
Alucard from Castlevania. Especially if you factor the radio drama into account.
Beruka, who has a huge Dark and Troubled Past that more than once comes back to haunt her, but she remains stonefaced and strongwilled. Even in the cases when she defrosts.
Flora hid the fact that she was being held prisoner by Nohr for years, never telling the Avatar, or Jakob, or even Felicia. Even after she escapes her captivity, the only one she reveals the truth to is Jakob, who she is prepared to either kill or be killed by.
It is entirely possible to interpret the Grey Warden as this. Even more so since the Warden's facial expression is rarely ever anything but The Stoic. One notable exception occurs in the Human Noble Origin after finding the Warden's murdered nephew and sister-in-law.
Cammy White, when she's mid-awakening from Killer Bee to human being and starting to question her actions and orders.
Final Fantasy X: Auron. At first, he comes off as an aloof, stoic mentor. Then comes the backstory. He started out as an ostracized monk and decides to go on the pilgrimage with Braska and Jecht because he had no other purpose in his life. One of his best friends from this time is later introduced as a corrupt Yevonite, and while he is killed, Auron is visibly angered by this. When the three are told by Yunalesca that the Final Aeon requires the sacrifice of both the summoner and one of his guardians, Auron relents, but fails to convince Braska and Jecht. It then turns out that this is all a lie, as the Final Aeon that kills Sin becomes Sin. Enraged, Auron attempts to avenge his fallen friends, and Yunalesca mortally wounds him. But Auron, being aDeterminator, instead reforms as an unsent, and in a heartbreaking display of resolve, kick-starts a good majority of the game's plot by crossing over to Dream Zanarkand and watching over Tidus, hoping to guide the next generation to finally end this terrible spiral of destruction. Auron's unexpected Not So Stoic moment, where he lashes out in an emotional frenzy at Zanarkand's projection of a younger him trying to get Braska and Jecht to not go through with the Final Summoning just shows how profoundly this event affected him, and his attempts toultimately atone for it.
"Dammit, Murai, It doesn't matter! If I have to stay in this god-riddled land of lunatics until I drop dead of—of—sheer frustration, then that's just life! I'll get over it! Not everybody gets to go home!"
Jerkass Woobie: Peter Venkman is a bit conceited and abrasive at times, but he had a rough childhood and it's often difficult to not feel sorry for the misfortune Slimer puts him through.
The Woobie: Slimer in some of his focus episodes, especially in "Slimer, Come Home", where he runs away and leaves a letter telling the Ghostbusters that he can't bear to stay with them if he continues causing them trouble.
YMMV/Shadowhunters: Every main character. And most of the recurring characters. This show does not give anyone a break.
Jerkass Woobie: There is a murder in which a business tycoon is killed on a boat (the infamous Hatamoto Family case). One of the suspects, his eldest granddaughter Akie, is an absolute Rich Bitch, surpassed in obnoxiousness only by her husband Tatsuo. She becomes a Jerkass Woobie when Tatsuo says terrible things about why he married her (Akie's little sister Natsue turns out to be the heiress, so Tatsuo openly says he only married her for the money much to Akie's horror), but then she cries heavily when he becomes the next murder victim. She's even seen cradling Tatsuo's lifeless body in her arms.. As much of a bitch as she is, well... no one deserves that.
The Woobie: Shinichi-Conan, Ran and Ai can be woobies at some point (certainly the O Ps and E Ds delight in depicting Ran as being all sad and torn up because she's been kept from Shinichi for so long).
Jerkass Woobie: Alia. We don't know much about her life prior to quantum leaping, but she's a particularly duplicitous piece of work in "Deliver Us from Evil." That said, as the Evil Leaper episodes progress, it becomes clear that her only "friend" is a sociopathic hologram, that she's been conditioned to think that evil acts are her eventual ticket home, and that any failure on her part will be met with torture and/or termination. By the time of her HeelFace Turn, she's shucked off the "jerkass" part and has become a straight-up Woobie.
The Woobie: Sam and Al so much, at least in their original backstories:
Sam loses his father and brother when he's in his late teens and his sister marries an abusive husband. His fiancée leaves him at the altar on his wedding day. And thanks to Chronic Hero Syndrome, he's left bouncing around in time.
Al's mother leaves him at a young age and his father is forced to emigrate to find work, leaving Al in and out of an orphanage. His younger sister dies in an institution and he loses his father. After joining the Navy, he ends up missing in action and his first wife, Beth, assumes him dead and marries someone else, leaving Al spending the rest of his life attempting to fill the void.
Jerkass Woobie: Louise is quite mean to Thelma - even going so far as to blame her for Harlan's attempted rape of her. But it's all but said she's a rape victim herself, and she's the only one who expresses more angst at running away than Thelma (who appears to find the whole thing liberated).
Even though he may not be as much as a jerk as this trope would imply, Samekichi is this. At first the game plays it like he's either the anti-hero or a villain in the making, with nearly everyone but Wadanohara treating him like a traitor. It doesn't help that he attacks Wadanohara and her familiars twice. But then you find out he's been purposely pushing Wadanohara away from him for a while now in a desperate attempt to keep her happy and safe, not caring that it would potentially ruin their friendship and earn him the disdain of the entire ocean. He's also the only character who was aware of the Big Bad's plan from the beginning and he's been trying his best to stop it without getting Wadanohara involved. So everything he's been doing and does in-game has been an extreme emotional toll on him, but he willingly puts himself through it for Wadanohara. Seriously, you can't help but feel even a little sorry for him.
Poor Blake goes through a lot of shit throughout the game. Unable to protect Jessica from an abusive teacher, his wife died from childbirth, chased by crazed cultists, beaten and bruised, crucified, raped by the leader of the Heretics — it's a surprise if he hasn't already lost his mind. A valid argument can be made that, during the events of the game, he has.
Lynn as well. Gets separated from her husband, gets tortured and pregnant, is forced to watch her husband get raped and finally dies a painful death.
Ethan as well, due to his backstory and being one of the few people who are nice to Blake, only to be killed by Marta.
Jessicas mother died when she was young, leaving her in the care of her (implied to be) abusive father. Her teacher then sexually abused her over a long period of time, later murdering her and framing it as a suicide. She was no older than thirteen.
Branson, oh god Branson. Come Season 3 he's exiled from Ireland (because he burned down an aristocratic Anglo-Irish family's castle), separated from his family, trapped in the house he tried to escape from, lost his wife, (the woman he spent six years waiting for) and left alone with a new-born baby.
Now he's also lost his brother-in-law/best friend who was the only one who understood him. And taken advantage of by Edna.EdithEdithEdith!
Casey was woobified almost immediately upon her introduction to the series, by both her backstory and the traumatic cases she worked. One episode even had her beaten into unconsciousness. By season 9, her crying episodes were a frequent occurrence.
John Munch's last words to his father before the latter killed himself were that he hated him. He has regretted this ever since. His uncle appeared in one episode only to go insane from depression and kill a man.
Don Cragen lost his wife in a plane crash and is an alcoholic.