Sakura (a boy, mind you), the main character of Bludgeoning Angel Dokuro-chan, is a particularly good example. He gets killed and revived several times per episode in the most brutally over-the-top ways possible.
At least he isn't the only one to suffer: The angel Sabato, who's introduced in the second episode, has to suffer a lot of misery and hardships after she fails to kill Sakura.
Tower of God: Ship Lee-Soo and Parakewl. One because his reactions are just to funny and the other because he just has it coming.
Mikuru from Haruhi Suzumiya eventually ends up being God's literal chew toy◊... and God is a mix of Genki Girl with Jerkass (and in the beginning, much more the latter than the former). In the opening, she cries as Haruhi forces her to be a cheerleader. She can go either way in The Woobie Vs. The Chew Toy debate, depending on how sadistic the viewer is feeling at any given time, or how serious Haruhi's abuse of the moment is.
The computer club president is a much straighter example of this trope.
Kon from Bleach. He is the right size for it and constantly fails to be cool. He's is literally a chew toy (or a doll), anyway.
The main cast of Slayers gets treated this way in some fashion, save Lina the heroine, but the worst of it is heaped onto Amelia. Compared to her other companions, whenever she has a say in something, she gets ignored, is thrown around by enemies a lot, gets pointed out for the dumbest things (the end of the first anime series had Copy Rezo point out her tendency to point at others, just to humiliate her), tends to be dismissed when she gets hurt unless the situation is dire (no one seems to care in one episode of the second series when she takes a Brass Racket ball to the face)...even idiotGourry, being a skilled swordsman, has an easier time than she does, save for when Lina is beating him up.
Taken Up to Eleven in the Slayers Premium movie, where she spends the final third of it alone on an island, unable to speak. Zelgadis assumes she left on her own and goes his merry way when the movie ends.
Junjou Romantica: Takahashi Misaki, who is the love (and jealousy) interest for an entire clan.
Jaken, Sesshomaru's impish retainer, on InuYasha is forever being abused by his "Master". (Drowned, stepped on, headbonked, etc. Although he's actually fairly good at defending himself from others who mean him harm.) Myoga, the titular character's flea-demon advisor, fulfills this trope as well (for Inuyasha), but once in a while, Shippo may get thrown (literally!) into the role.
Sesshomaru's abuse of Jaken in his early appearances was threatening to kill him; it was other characters that beat up Jaken. But as Sesshomaru become less of a villain and started to care about Jaken after a fashion, his abuse of Jaken started to descend into slapstick beatings and verbal abuse.
Keitaro in Love Hina. He moved in to the place of his childhood, only to find it to be turned into a girls-only pension. When he is accepted as a legitimate resident (it's a long story) he is then forced to work like a slave for roommates who constantly beat him up for his bad luck, when they're not doing it for fun.
In xxxHOLiC, one Watanuki Kimihiro never seems to get a break. He's antagonized by monsters normal people can't see, degraded and belittled by his employer, constantly having to be rescued by his "rival" and to top it all off, he never gets the girl.
It's later either justified or made worse, depending on perspective, when it is revealed that he is literally not supposed to exist, and he knows it. Those invisible horrors stalking him? They're only doing it due to his supernatural nature combined with subconscious suicidal desires.
Lancer from Fate/stay night may have been a credible threat in the original work, but subsequent sequels and fan works often portray him as largely useless, particularly whenever Archer is around. In the recent Carnival Phantasm series, he's killed off more or less Once per Episode, and his 'guest appearance' on the (fake) preview for Arcueid's magical girl show has his silhouette dramatically show up... before instantly being hit by a car. Assassin has been entirely replaced with a cardboard cutout in the first episode of CP.
Mesousa from Pani Poni Dash!. Not an episode goes by without the universe inflicting some form of misfortune on him, from being attacked by malevolent soda cans to being stranded in space to being used as a literal chew toy. Appropriately enough, his name means "weeping rabbit".
Normad, a Deadpan Snarker AI stuck inside an immobile plush toy in Galaxy Angel, is generally abused and mistreated by every single member of the cast (usually due to his snarking pushing somebody's Berserk Button), including Vanilla, whom he worships despite the fact that she drags him around on the ground by his tail, uses him as a shield whenever needed, and has resorted to eating him whenever she's on the verge of starvation.
As a Continuity Nod, Mimolette, a bizarre floating cat-head thing from Galaxy Angel Rune gets much the same treatment, despite being generally nice and helpful to the girls. Nearly every single episode ends with a freeze-frame of whatever horrible suffering was piled upon him, following the Post Episode Trailer.
Kiyone from the Tenchi Universe branch of Tenchi Muyo! endures constant humiliation due to being partnered with Mihoshi, who is the personification of ditz.
Mic Sounders The 13th in the first half of GaoGaiGar lasts, on average, about five seconds in any real battle until he gets swatted away like a fly. In the second half though, the universe makes it up to him by giving Mike a System Change transformation powered by The Power of Rock, and the most potent Weapon of Mass Destruction in the series.
This is sadly Truth in Television, as Eastern Europe's history is full of Chew Toy situations. Usually, only Poland gets any recognition.
Metallis in Magician's Academy. Not an episode goes by where some misfortune befalls him. All of his magic was drained by Suzuka's first in-show appearance, he was tied up by Synclavia and was the one who released the Hard Gay angel onto the school. After Metallis finds love, the role of Chew Toy shifts to George.
In Excel♥Saga, Excel normally tries to hold down a job while completing a mission for her beloved Il Palazzo, but her hyperactivity and stupidity means she always fails at both, and destroys wherever she is working.
Spandam: You hate him from the start of the story, being physically weak and feeling strong only because he has strong people working under him, he ruined Franky's childhood by killing his mentor, and he doesn't seem to believe lowly pirates, scum of the sea can possibly be superhuman enough to defeat CP9, and is under the misconception that Luffy only killed 5 of his guards, with no idea that Enies Lobby has actually been invaded by pirates, and then of course, he is punched and crushed with an elephant by Franky (It Makes Sense in Context) then is slapped repeatedly by Robin, while later having his spine broken by her. And after watching the whole "Enies Lobby" Arc, you'll love to watch it, along with his other mishaps during the arc.
Hol Horse from part 3 of JoJo's Bizarre Adventure. In his first appearance he was quite a threat, as he almost kills Avdol, but is forced to run away when his backup is beaten as he's too much of a coward to fight by himself. The next time we see him he's forced into an Enemy Mine situation thanks to his previous actions, but once again gets away, this time with the heroes' car. The last time we see him he's teamed up with Boingo, trying to take advantage of the latter's powers of prediction. He screws up and winds up shooting himself in the face with his own gun.
After being disgraced by Edward of Fullmetal Alchemist, Yoki spends the rest of the series being on the receiving end of constant humiliation, from being beaten up by refugees, practically being Scar's slave and being a useless hostage because no one cares what happens to him. It actually gets to the point that everyone (including the reader and Yoki himself) is surprised when he saves everyone from a really nasty Big Bad with some well-timed Car Fu.
In the first anime, he's spared this humiliation; instead, Lust kills him to set off a riot.
Arguably, Ranma of Ranma ½. He gets a fair amount of Throw the Dog a Bone moments, but examining his past makes one wonder just how much his family must have pissed God off to warrant the stuff he goes through. Some of it is his fault, some of it is Genma's, but a lot of it is just implausibly bad luck.
Takeru in Rokushin Gattai God Mars is a terrific example. The head Bad Guy sends him to Earth as an infant such that, once grown up, he will destroy the planet. But things go wrong - relatively speaking - and Takeru, now grown up, decides against the plan. Whereupon the Bad Guy sends out assassin after assassin to kill him and, in just about every episode, he's beaten, burned, frozen, zapped, electrocuted, asphyxiated to within a centimeter of his life, at which point the title robot arrives to save him. In the second half of the 64 episode series, he's even stuck with a psionic device which drains part of his life force if he attempts to use his powers. It doesn't get much worse than that. Oh and, he knows that, if he does die, the super-bomb in his guardian robot will blow up the planet.
Originally, Higurashi's chew toy was Satoko. However, by the fourth arc, she's rescued from the bin, and gained a large fan base. She's now just The Woobie. She can go between being a chew toy and a woobie depending on the mood of the show at the time.
In Umineko no Naku Koro ni, Rosa gets the worst of this. The only time she's made it past the second twilight was EP2. And frankly, dying horribly is probably an improvement over what she goes through in some of the other arcs, especially EP4, when Maria kills her over and over again with magic in the most painful ways she can think of as a horrific version of Calling the Old Man Out. Unlike Satoko, she's still not The Woobie, given her relationshipwith her daughter.
Katsuya Jounouchi/Joey Wheeler of Yu-Gi-Oh! almost constantly gets this treatment from Seto Kaiba.
Yu-Gi-Oh! GX: Daitokuji-sensei literally ends up as this after his death due to his cat Pharaoh often chasing him around and swallowing him.
Shimon of Tengen Toppa Gurren Lagann Gurren Gakuenhen has all of the qualities of The Chew Toy: his prayers for a normal life get answered with Kamina doing a flying kick through his bedroom window (and this is the most normal entrance into Shimon's room Kamina will ever perform), accidentally gets involved with a girl who regularly draws him into bizarre situations, gets chased by sharks for most of the Beach Episode, gets blown up by landmines repeatedly, and much much more. The entire universe seems to exist to make try to hurt Shimon. The only things that separate him from an ordinary Chew Toy is that he is the main character of the story, and the fact that he manages to take a speech about his constant misfortunes and transform it into a Badass Boast and has an Awesome Moment before the end of the series.
Yukinari of Girls Bravo. Though some fans differ on whether or not it falls into Dude, Not Funny! at times considering how Kirie, who is supposed to be his best friend, beats him up to a brutal degree constantly.
Kelly from Transformers: Robots in Disguise is a female version of this trope. She's not clumsy or incompetent, just incredibly unlucky. No matter how remote her vacations or how many cars she buys, they will always be ruined by the Transformers on a regular basis. To add insult to injury, it's seldom as a result of collateral damage and instead of incredible misfortune.
Episode 1: Fired out of her SUV via Ejector Seat. Episode 2: Car eaten by robotic shark, etc...
Sky-Byte was a villainous example, with his tendency towards panicking, and getting blown up. In one episode Megatron mistakes him for an Autobot and blows him up twice.