Touhou fandom being what it is, many characters get this at different times. Hong Meiling (who's always suffering Sakuya's stabbity wrath for sleeping on the job and allowing Marisa into the Scarlet Devil Mansion to steal Patchy's books), Reisen Udongein Inaba (who's always getting punished by Eirin for Tewi's pranks, in addition to the sadistic attentions of Kaguya and others), and Mystia Lorelei (who has to deal with Yuyuko and other youkai always trying to eat her) probably get the worst of it, though.. Borderline canon in Reisen's case, too.
Special mention goes to resident Green-Eyed Monster Parsee, whose entire existence revolves around her being extremely, miserably jealous of everyone, and her backstory is implied to be a major Tear Jerker. All of this is completely Played for Laughs by the fandom; it is telling that "paru paru" (derived from the Japanese spelling of her name) has been adopted by the fandom as the Un Sound Effect for jealousy.
Many characters in the Disgaea series have moments of this:
Disgaea 3: Absence of Justice has Almaz as the chew toy. He gets his title stolen, will slowly turn into a demon, is shot by his Love Interest when she takes him for an enemy, nearly dies from poison, and other things. In the Almaz ending, he becomes Overlord against his will and gets ditched by the party. In the normal ending however, he gets the bone thrown to him.
He's so much of a chew toy that he gets an entire song about how unfortunate he is in the former of the two mentioned endings.
Then there's the Prinnies, who are an entire race of Butt Monkey Chew Toys. They'd be sympathetic if they weren't mostly lazy reincarnated criminals, a fact which makes the fact they are LIVING GRENADES utterly hilarious.
Etna in the second half of Disgaea 2. Come on, she loses all her amazing levels, becoming a lv1 wimp that can't even beat Laharl (the first one she wish to kill in her list). And, the worst of all, her own prinnies mock her and go away. Do you know anything more humiliating to Etna?
In Knights of the Old Republic HK-47 seems to get smashed up, shut down and locked into a warehouse, zapped with ion beams, or be disassembled and have his parts shipped to opposite corners of the galaxy quite frequently.
Sandbag from Super Smash Bros.. Sandbag is a semi-sentient, well... sandbag, whose sole purpose is to be beat up upon (Its description as a trophy even states this). In Melee and Brawl, there exists a "Homerun Contest", where the player would beat up Sandbag, then see how far they could hit it with a Home-Run Bat smash, which is one of the hardest hits in either game. Furthermore, Sandbag, when it appears as an item in Brawl, will drop a bottomless supply of items when beat up upon. Sandbag also spawns in the Brawl online waiting room for the player to attack.
Sandbag doesn't actually mind being beaten up, though. It oddly enjoys it. He's something of a masochist.
The village of Mile in Phantasy Star IV. The crops have all withered and died, the ranch owner can't seem to catch a break, and the village is steadily being covered with sand due to the encroaching quicksand field nearby. It doesn't help that they're located right across the sands from Zio's Fort. In the endgame every single inhabitant is wiped out by the Black Energy Wave emanating from the dimensional rift that the Profound Darkness has ripped open.
In Live A Live, the Watanabe father-and-son pair lose its father or both in every single chapter. And how easy it can be seen depends wildly between chapters, from the Mecha chapter featuring a little boy named Watanabe wondering where his father is, to the Wrestling chapter just about requiring you to use a cheat code to allow you to trigger the scene.
Malygos and the rest of the Blue Dragonflight in Warcraft. Without fail, everything Malygos has tried to do in the last ten thousand years or so has turned into a catastrophic event for his flight and sometimes for the world as a whole. Small surprise he ended up going a little insane... and when he recovered and tried to stop the madness mortals have unleashed with magic, the other dragonflights ally to fight, and ultimately kill, him.
He did, mind, decide he was going to do that by killing every last magic-using mortal. Leaving aside the minor genocide aspect, this does have the small objection of guaranteeing the mortals of Azeroth become too weak to defend against the Burning Crusade. Oh, and there's also the part where one of his other plans is going to blow up the planet. He really didn't get much less insane at all.
The Elven Race of the Disciples series gets well and truly hammered throughout their history. They were the first victims of the Legions of the Damned in the backstory, and fled into the Mountain Clan's territory to escape the onslaught. The Dwarves, thinking the Elves were invading, attacked them right back. The Elves' patron God, Gallean, went to the Dwarve's god, Wotan, and demanded some repayment for the mistake. Wotan killed him for his troubles and threw his heart into the sun. It got worse because from there, when Mortis, Gallean's wife, eventually got around to sending an Undead army on their lands as part of her plan to resurrect Gallean, in which they lost their Queen, and then they suffered the double-whammy of their High Prophet and another Queen falling to two different invasions of the Legions of the Damned, as part of their scheme to free their own god, part of which involved the Elve's lands getting turned extra-crispy, and meanwhile the newly revived Gallean went insane and went away for a while when he rejected Mortis. It was so bad that Strategy First gave them an expansion pack all forthemselves, during which they decided to get revenge on the human Empire of all people, the only people who never wronged them, at least not in a way that's not All There in the Manual.
Punch Out regular Glass Joe, with his 1-99 record and feeble attacks, as well as being something of a fan favourite is a perfect example. It has an even worse one, 1-99 that means somebody out there actually lost to Glass freakin' Joe. Word Of God for the Wii version says it was Von Kaiser, who decided he could beat Joe with his mustache and got his face in the way of Joe's fist, ruining his career forever. But when you get to Title Defense...
Super Punch-Out for the SNES gives us Joe's student, Gabby Jay. Also 1-99, with Glass Joe being his only win.
Winston Payne in the Ace Attorney games. In every single appearance, he is always the first prosecutor the player faces and is usually the easiest one to win against due to flaws in his logic and reasoning and he is quick to make excuses or give sloppy explanations when he is losing his case. Payne gets treated so badly from the story writers that in the 3rd game, he loses most of his hair after losing his case to Mia Fey several years before Phoenix Wright became an attorney, and in the 4th game, the story in the first case shifts away from Payne and onto Phoenix Wright and Kristoph Gavin, causing Payne to say in the end "What about me!? Don't I get to prosecute anyone!?"
The Black Baron of MadWorld has the honor of introducing the newest death trap in each Bloodbath Challenge... and the misfortune of being used to demonstrate each and every one, courtesy of a tall woman in a spiked bustier. Did I mention that he's also the Final Boss?
Nathan Drake from the Uncharted series has a habit of taking lots and lots of physical abuse. For example, the second game opens with him shot and in a wrecked train hanging over the edge of a cliff.
In The Sims 3 you can design your own Chew Toy by assigning a Sim either the Unlucky or the Loser trait. (Bonus points for assigning both) The Sim will forever be surrounded by bad juju but will be literally unable to die by anything except old age.
Norman Jayden from Heavy Rain. Every chapter he's in involves withdrawals and attacks, both physical and verbal.
Brad Vickers, helicopter pilot for S.T.A.R.S. Alpha team in Resident Evil. He's basically shown to be a Dirty Coward in the first game, abandoning his teammates to the horrific mansion, only returning at the very end. In RE2, he returns in the form of a zombie who the player has to kill if they want to acquire the key to the locker where Claire or Leon can change their outfits, and even worse, RE3 shows how he was zombified — by being killed by the Nemesis.
Mitsumoto from the Izuna: Legend of the Unemployed Ninja series is casually dismissed, ignored, or made fun of by all those around him, including the rest of his own party (Izuna, Shino, and Gen-An). This extends to his Player Character status in Izuna 2, where he can use every available weapon but isn't good with any of them, and can form a powerful tag attack with any of the other characters...which always results in him getting hurt and taking damage. Ouch.
Thrillville has Mortimer be one because of his crazy expirements.