In the Manhua Bloodline, there are plenty of characters who can be considered this. The starring one is the series' main character, Lilo I. Having a wish to live a human life end in disaster, losing her father in the process, and many friends to the fanatical Shengdi organization. She spent an entire Time Skip waiting desperately for her father to come back and gaining help results in attacks that respark memories of her horrible past few years. So sad...
Then, there's Ye Lai. Being an annoying Cute Ghost Girl, she always felt in love with her alive younger brother Ye Ren. Then after such Heel Realization, she is impaled In the Back by a classmate of his who she also loved (depspote him not knowing). Her last few moments with Ye Ren are as depressing as a fan ofthe series could possibly get.
One of the antagonists, Posui Nangua is also considered a woobie. After being tried a heretic, he's forced to wear a strong Power Limiter while going in missions helplessly with his superior. And even when his powers were needed, he is totured and restrained again afterwards.
The Girl in the Slayer Jacket from the Pig Destroyer song of the same name. Just go read the lyrics, man.
Dr. Light in The Protomen's rock opera. That poor man spent pretty much his whole life enduring tragedy after tragedy, the abbreviated list including the death of his love, being framed and arrested for said killing, narrowly escaping the death sentence, getting chased out of town by a lynch mob that believed he deserved the death sentence, sending an innocent teenager to his death for a plan that didn't work anyway, losing his first son to the tyrannical dictator suppressing the city, having to watch his second son kill his first, then watching his second son abandon mankind to it's doom. Someone give the old lump a hug already.
On that note, Protoman himself counts. He might not think humanity's worth saving (in fairness, they did just watch Wily's robots 'kill' him) due to their refusal to fight for themselves, but he wants so desperately to be proven wrong. Especially in "The Stand", where humanity proves him right, again, and he's genuinely heartbroken- "They'll watch you die to save their lives! They will not stand here by your side..."
The subject of the song "Carry You Home" by James Blunt. The poor kid's apparently never had any friends, and seems to have leukemia or something. The only one with her when she Shuffles Off is James.
The runaway girl from Nuclear Death's "Days of the Weak". Also a bit horrifying.
The eponymous subject of Blutengel's song "Broken Girl".
All three girls mentioned in the song "Runaway Love" by Ludacris and Mary J. Blige.
The titular character of The Who's Tommy. First he's rendered deaf, dumb and blind after he witnesses a murder as a young child. Then he gets tortured by his cousin. Then he's given tons of drugs by the 'Acid Queen.' And then he gets molested by his Uncle Ernie. Eventually his sight, voice, and hearing are restored, and he becomes a Messiah figure to the fans he gained playing pinball. His followers turn on him shortly after.
Richard Marx's song "Hazard" portrays a guy who grew up with his single mother in a town where everybody refused to believe that there was any good in him. Eventually, he meets a woman who sees him for who he really is, but when she is murdered, the whole town naturally blames him. But the music video shows that the sheriff killed her, seeking to blame it on the protagonist and get rid of him for good. Fortunately, they can't prove him guilty, so he is released, and he packs his bags and leaves town for a brighter future.
The "Wild Eyed Boy from Freecloud" (Space Oddity) is an innocent "missionary mystic of peace/love", but feared, imprisoned, and sentenced to hang by the denizens of a village simply for his oddness. He accepts this fate, but the titular mountain sends down an avalanche to save him, despite his cries for it to stop — he lives, but the village is destroyed and he's in tears as he heads home.
The protagonist of "Jump They Say" (Black Tie White Noise) is a mentally ill man who is Driven to Suicide by — depending on how the lyrics are interpreted — the voices in his head and/or a society that doesn't understand him or care what becomes of him. The video expands on this by establishing him as a businessman (played by Bowie) who has done no one any harm, has not rocked anyone's boat, yet is taken captive by his peers and subjected to shock therapy...paving the way for his fateful jump. (Reality Subtext: This song was inspired by the suicide of Bowie's schizophrenic half-brother.)
Julie, one of the protagonists of the '70s pop song "Run Joey Run" by David Geddes. Her dad finds out she and the eponymous Joey have been up to things that the dad doesn't approve of and beats the crap out of her. Then when Dad goes hunting for Joey, rifle in hand... things got worse for poor Julie. The song's a bit on the manipulative side, but oh, how the listener feels for Julie! (And — the hell? This song was performed on "Glee"?)
The title character of the 1970 hit "Jennifer Tomkins" by Street People. She's abandoned by her alcoholic father, her mother dies, she's forced into child labor, then when she grows up she dates a jerk.
The old country standard "Nobody's Child". It's about an orphan. An orphan that no one wants to adopt. Because he's blind.
The titular character in "Little Susie" by Michael Jackson.
New The Daily Show correspondent Kristen Schaal is making a career out of being one of these. See here what happens to her when she learns the truth about Chinese female babies. In another segment, she was forced to strip off an article of clothing for every baseless accusation made against a presidential candidate. Needless to say, that episode, everybody found out that Kristen wears a Wonder Woman costume under her suit.
Bizarrely enough, her stand up act runs on this as well.
Doll Face. Poor thing. Probably comes second to WALL-E on the 'robots you most want to hug tightly' list.
Kermit the Frog off The Muppet Show. He tries so hard to be cheerful, friendly and positive that when he does become sad or even just exasperated by the madness going on around him, you just want to give him a hug.
His friend Fozzie Bear probably falls under this too. He just wants to be funny, but he keeps falling on his face.
Martin Crieff in Cabin Pressure. The poor guy lives in an attic, lives in Perpetual Poverty and doesn't get paid to fly, but he does anyway because it's the only thing he's wanted to do since he was six years old. His father always disapproved of his dreams, and passed away four months before Martin got his pilot's license and proved his father wrong. Oh, and what does he actually do to support himself? He does removals with the van his father bequeathed him in his will, rather than the 5000 pounds each of his siblings got. So, even though he did become a pilot, his father was still right about him. All of this is played for laughs.
Netherlands in the FIFA World Cup. They're constantly one of the best teams in the world, but the three times they've made it to the Finals, they've always been beaten, usually in a shameful way.
Cavalier King Charles Spaniels. Nearly all of them are afflicted with cardiac and/or skeletal problems, as well as syringomyelia, which in humans is described as one of the most painful conditions in the world. Despite this, they're known for their incredibly friendly and gentle demeanor, even with children.
David Ferrer. He's one of the most likeable and humble guys on the men's tennis tour and has a well-earned reputation as The Determinator against 99% of the tour, but his fighting spirit gets broken over and over again by the remaining 1% of the tour and it's tantamount to watching an adorable terrier start out yipping eagerly and end up a whimpering wreck on the floor after the inevitable beatdown. His Woobieness probably reached its peak during the Miami Masters final against Andy Murray, where the sight of him hiding his face◊ after he let a match point for his biggest-ever win slip away and his tearful apology to the crowd afterwards, "I'm sorry. I'm so sorry. One point...," made dozens of fans want to give him a giant hug.
In Dino Attack RPG we have Kate Bishop. Oh boy... Kate Bishop, the poor innocent teen who was never really cut out for life on the battlefield, not to mention had a very difficult childhood because of massive debt her mother owed various people as a result of her brother performing a lobotomy on himself. PeabodySam even turned her crying into a Drinking Game just to lighten the mood.