Tortured Abomination

Mostly, an Eldritch Abomination is something like what we call evil, and it has a plan and wants to inflict pain. Either that, or it operates on a value system completely alien to ours, and inflicting pain is a completely unimportant by-product. Sometimes, however, it is just as unable to comprehend itself as you are, and it's filled with pain, horror, and disgust for itself. It just wants to be put out of its misery.

What happens when an Eldritch Abomination must scream, but rather than being trapped with no way to fix it, they can (and do) lash out. They may be trying to get help and not understand that they're hurting people, or they're trying to provoke someone into killing them, or they just want everyone else to feel as bad as they do. They'll eventually meet The Hero who fights back and releases them from their pain (if they get a happy ending -- living on like this is a much worse fate). The hero may or may not realize after the thing is dead that he just did it a service.

Not to be confused with an Eldritch Abomination which is being tortured by some other entity.

Prone to Monster Sob Story, Cry for the Devil, Alas, Poor Villain, Apologetic Attacker, and Mercy Kill (on the receiving end). The Monster From Beyond the Veil varieties of Came Back Wrong can be this; can also be the end result of The Punishment or To the Pain. Often found in a Tragic Monster. This is not just a mutilated or disgusting thing that wants to die -- it must be able to do damage.

Anime and Manga

 * In Fullmetal Alchemist, the Chimera acts like this, even mentioning that something feels wrong. (Un?)fortunately for it,
 * While he was simply evil incarnate in the Japanese version of Digimon Adventure, the dub attempted to turn Apocalymon into one of these. The change was generally not well regarded by the fandom.

Comics

 * Anthrax in Requiem Chevalier Vampire is a humongous mutant who's essentially unkillable as he regenerates all wounds. However, when Requiem uses a spell on him that reveals his deepest desires, he proceeds to jump off a skyscraper.

Fan Fiction

 * The Bleach fic "Winter War" has Aizen doing this to . As if merging them with   wasn't bad enough, just wait until we see   because of how badly he got broken, yet still all he wants is to.
 * Imperfect Metamorphosis has.

Film

 * Frankenstein's Monster, specifically in Bride of Frankenstein where he blows himself and his bride up with the comment, "we belong dead."
 * In the 1986 remake of The Fly, the monster  is confronted by a shotgun - wielding , and   Tear Jerker moment, indeed.
 * According to Word of God the Monster in Cloverfield was a terrified infant, looking for its mother.

Literature

 * Discworld:
 * The wolf in Witches Abroad, which was once a normal wolf but was twisted by the villain's magic, making it intelligent, dangerous, and horrified by its own existence. It's generally a bad idea to grant sapience to an animal that spends most of its waking life hunting other animals.
 * The Hiver in A Hat Full of Sky is a bare awareness that is terrified of its awareness of everything around it and seeks refuge in living beings' more limited minds, in which it due to its nature unintentionally becomes a terrifying possessing presence.
 * Frankenstein's monster in the original novel is a very intelligent creature that is fully aware of how hideous and repulsive he is. Anything wrong he does is borne entirely out of bitterness from how people treat him.
 * The villain of an Astrid Lindgren story has a heart of stone (literally, it seems), suffers from it, and begs to be killed at the end.
 * Haliax in The Name of the Wind is a perfect example of this trope.
 * Nyarlathotep from the Cthulhu Mythos may be an example. It is known that he despises the Outer Gods, but his bery nature (being the personification of their will) would make him unable to go against their will. So it is theorised by some that his habit of spreading chaos and generally being a dick is caused by him taking out his frustration with his "job" on those weaker than him.

Live Action TV
""Technology using the one thing a Dalek can't do--touch. Sealed inside your casing. Not feeling anything... ever. From birth to death, locked in a cold metal cage. Completely alone. And that explains your voice! No wonder you scream.""
 * The minotaur from the Doctor Who episode "The God Complex."
 * Also, Doctor gives this little hint about the Daleks in Doomsday:


 * In the Japanese Tokusatsu Show Garo, the Monsters of the week are humans possessed by demonic entities called Horrors. Whenever a human is possessed by a Horror, they will feel excruciating pain. They all get the Mercy Kill.

Video Games

 * Sin from Final Fantasy X.
 * In Brutal Legend, the summonable but uncontrollable Tainted Coil unit named "Bleeding Death" may be this: it is a perversion of nature (not to mention the single strongest non-Hero Unit in the game), which is slowly dying, so its attacks are merely expressions of its agony.
 * The zombies from Half Life are humans who have been turned into People Puppets and mutated by the parasitoid headcrabs attached to their heads. In the second game they can be heard screaming for help as they attack you (although it's implied this may be a subversion - that the headcrab is mindlessly parroting the last words its host made).
 * Many Silent Hill monsters can be interpreted this way.
 * Giygas of Earthbound : "...It hurts, ...it hurts... Ness, Ness, Ness, Ness, Ness..."
 * The character of Harold from the Fallout series. He's a mutated human, and one of the only characters to appear across multiple games. By Fallout 3, his mutation has progressed to the point where his form has merged with a tree, and he's rooted to the dirt. Surrounded by the only patch of green vegetation left in the entire Capital Wasteland, he is worshiped by a naturalist cult called the "Treeminders." Sadly, Harold has had enough of life, and wants to die. The Treeminders misinterpret his pleas for release as "tests of their faith," and do everything they can to nurture him and keep him safe. It's up to the player character to decide Harold's fate.
 * In the remake of Resident Evil, is a twisted mockery of a woman who's been trapped in a constantly-mutating, undying body for thirty years, and was driven insane by her ordeal a long time ago.
 * The victims of The Many in System Shock 2. They can often be heard begging you to run or to kill them even as they attack.
 * Gergoth in the Castlevania series is mentioned in the in-game bestiaries as once having been gentle, but having lost its mind to insanity due to torture and imprisonment.
 * The Forgotten one is also a good example.

Web Original

 * More than a few SCPs, especially the ones that are or were humanlike. On the more tortured end of the scale, you have ones like 191 (a little girl who was sloppily turned into a cyborg, who can no longer speak and seems to be in constant pain); on the more abominable end, you have 682, a monster that wants to kill everything because it finds life on Earth horrifying and disgusting.

Western Animation

 * South Park: Stan falls in with a bunch of extreme environmentalists who marry animals. The "child" of such a pair - a man and an ostrich - can only say "kill me."
 * Not started outright in Generator Rex, but heavily implied; most people who've gone EVO seem to become insane, rampaging beasts, and generally seem very happy to be cured.