Villains can have a wide range of motivations. Some villains get sadistic pleasure from seeing others suffer. Others simply want the same things the heroes do: wealth, love, food, etc., but they lack the moral integrity, courage, or knowledge to be a heroic character.
This is a villain who poses a credible threat to an entire community, is miserable, and blames it on everyone else. They rationally want to "Put Them All Out Of Their Misery".
This character is not necessarily an Omnicidal Maniac, a nihilist who wants to destroy everything for the sake of destruction, nor a Woobie, Destroyer of Worlds who was mistreated, snaps, and lashes out on the world. This person is simply trying to cure an ailment, and are willing to go to any length to do it. While Put Them All Out Of My Misery villains are usually at least slightly sympathetic in the sense that at least their motive is understandable, they come off as jerks for putting their own misery ahead of others' safety.
There might be many reasons this villain believes he must cause trouble for others to heal himself:
Good Hurts Evil, so the villain seeks to destroy good first, in self defense.
The villain desires to alter some aspect of the physical world which he views as harmful to himself, and if others are harmed by the change, it's not his problem.
The villain finds some aspect of the heroes' society so fundamentally incompatible with their own beliefs, etc., that they declare war on all "normal" society.
The villain experienced injustice, and plans to rid the world of the society that caused it. Almost like Utopia Justifies the Means, but this time there's no Utopia to replace destroyed society.
Rokudo Mukuro from Katekyo Hitman Reborn! wants to cleanse the world of mafia (and then everything else) in blood due to his ''tragic backstory'. Also because he hates humanity. Either way.
Black WarGreymon from Digimon Adventure 02 wanted to destroy the Digital World because he thought that was the only way for him to understand his purpose in his artificial life and soothe his pain.
In the original, the final villain, Apocalypmon, was formed from the combined essences of every Digimon that inadvertently destroyed itself while trying to "digivolve" to a higher form. Somehow surviving in a miserable place outside of normal time and space, it sought to escape in order to make everyone else just as unhappy.
From Kurohime: Dark Zero who is really "Rei", the older brother of the real Zero wants to wipe out humanity because of the numerous sins he's seen them commit, and experienced on his own. Considering what his childhood was like, this is hardly surprising.
Ookami Kakushi gives us Sakaki, whose motivation stems from Type 4: His fiancee was murdered, and he received no cooperation from the authorities to find and punish the murderer—Nemuru Kushinada, who had to carry out the old laws on dealing with Kamibito who lost their self-control. This caused him to develop a grudge against the entire city of Jougamachi, and he ultimately attempts to flood the village at the end of the anime.
It happens under slightly different circumstances in the Visual Novel: Up to that point, he was just investigating the truth behind his fiancee's death. But what finally pushed him to it was learning that Kaori, the woman whom he had fallen in love with, had been taken away to become a "White Wolf Kannon", which he interpreted as a human sacrifice. Convinced that it was Jougamachi's laws that had taken away the women he loved, he planted bombs to blow up the dam and wipe away the city for good.
In One Piece, one of Enel's priests wants to stop suffering in the world and stop the fighting. How? By killing everyone.
In Trigun, anime Legato Bluesummers just hates humanity, including himself, and is loyal to Knives, therefore genocide. The manga version has a back story: child sex slave, whose response to discovering his psychic powers was to attempt to kill everyone he had ever met, instead of just his immediate tormentors. The delay this involved allowed them to figure him out and start raping him to death. Then Knives killed the building and everything in it. Except Legato.
First time was an accident. Second time, after the kid pledged his loyalty so touchingly, was on purpose. Legato honestly was better treated by Knives than by anyone else he'd ever known. Because Knives didn't-kill-him, and asked him his name, and let him follow. Therefore, Legato wants to Kill All Humans.
The King of the Night in Kore wa Zombie desu ka? just wants to die but Eucliwood won't let him so by God he will kill every last person on Earth if he has to to convince her to finally kill him.
Genkaku from Deadman Wonderland in reality he wants to save everyone from the burden of living by erasing them. This stems from a very skewed take on Buddhism: he was revealed to have been beaten and raped by a group of bullies who hung around the temple when he was younger; when the Great Tokyo Earthquake happens and these are trapped under the rubble he has an illumination of sorts and decides that it is best not to exist then to live in pain. He proceeds to butcher them all. Complete with a moment of Dissonant Serenity as he explains all this while covered in blood.
The motives of King Joseph of Gallia in Zero no Tsukaima can be explained as such. For a long time, he was overshadowed by his immensely talented brother and was intensely jealous of him. He thought he would feel better if he got his brother out of his way, but it did not work and he ended up becoming devoid of any feelings. And then he thought perhaps destroying the world would fill the void in his heart....
In Fairy Tail, Zeref decides on this course of action after observing the world for the last seven years and seeing that it is still a place filled with strife. His own powers making him an Enemy to All Living Things and a Walking Wasteland don't help. In his own words, "If the world continues to reject me, then I will reject this world." He's forcing a situation where his enemies will be forced to kill him or be killed. Eitheroutcome is fine by him.
Shiki gives us Motoko Maeda, who reacts to the death of her children at the hands of the vampires by burning down the entire village, just to get revenge on her father-in-law, whom she blames. She also sells out the vampire mother of her best friend to the vampire-hunters, despite the fact that said best friend's mother had never attacked anyone and never would, because she's angry that nobody in her family came back to her!
Mr. Freeze from Batman is a villain whose body has been altered in such a way he must be refrigerated to stay alive. Naturally, he would like to change Gotham's weather so he can walk around safely without all his life support gear (Type 2) but in many versions of the story he also is angry over the fate of his wife (Type 4).
Superboy of Earth-Prime, Superman of Earth-2, and Alexander Luthor of Earth-3 in Infinite Crisis - especially the first one.
In Hero Squared, Captain Victory hurt his girlfriend, so she became a supervillain and destroyed the entire universe. He managed to escape to another universe and found his non-superpowered equivalent; she followed. Caliginous has decided that life is nothing but pain, misery, cruelty and death, and should be ended in preferably the most all-encompassing fashion possible.
Azrael in Dogma, a formerly pacifist angel who was cast into Hell for refusing to fight in the war between God and Satan, tries to end the universe via a cosmic Reality-Breaking Paradox to end his suffering.
Once Azrael's been defeated, his former Unwitting Pawn Bartleby snaps, realizing that God has always favored man above angels like himself and striking back by attempting to fulfill Azrael's plan. Even his Ax-Crazy partner Loki turns on him, protesting that this isn't what he wanted. It doesn't go well for Loki.
Nero the Romulan, from the new Star Trek, REALLY wants Spock to understand his pain...by destroying his homeworld, as Romulus was destroyed in Nero's original timeline. And after Spock, the rest of the Federation is to get the same treatment, starting with Spock's mother's homeworld, Earth.
In Law Abiding Citizen, Clyde Shelton seeks revenge not only on the man who destroyed his family, but on the entire system that failed to convict him.
In the 2007 Beowulf film, Grendel was made somewhat more sympathetic with the inclusion of a justification for his attacks: somehow the acoustics of the mead hall meant that the revelry within was painfully loud for his sensitive exposed eardrum.
Kadaj from Final Fantasy VII: Advent Children wants to absorb all the people infected by geostigma into the Lifestream to join his "mother", Jenova. While he is a Remnant of Sephiroth, his amnesia made it appear that he sees that the end of all life on the planet as a GOOD thing.
While 'Dark Alessa' from the Silent Hill movie qualifies as Woobie, Destroyer of Worlds, her original, 39-year-old, now soulless body ends the film by finally getting her revenge on the cult who burned her alive by killing them all, with the exception of her mother, Dahlia.
Ducard: Only a cynical man would call what these people have "lives," Wayne. Crime. Despair. This is not how man was supposed to live. The League of Shadows has been a check against human corruption for thousands of years. We sacked Rome. Loaded trade ships with plague rats. Burned London to the ground. Every time a civilization reaches the pinnacle of its decadence, we return to restore the balance.
Wayne: Gotham isn't beyond saving. Give me more time. There are good people here.
Ducard: You're defending a city so corrupt, we have infiltrated every level of its infrastructure. When I found you in that jail, you were lost. But I believed in you. I took away your fear, and I showed you a path. You were my greatest student. It should be you standing by my side, saving the world.
Wayne: I'll be standing where I belong. Between you and the people of Gotham.
Ducard: No one can save Gotham. When a forest grows too wild, a purging fire is inevitable and natural. Tomorrow the world will watch in horror as its greatest city destroys itself. The movement back to harmony will be unstoppable this time.
Wayne: You attacked Gotham before?
Ducard: Of course. Over the ages our weapons have grown more sophisticated. With Gotham we tried a new one, economics. But we underestimated certain of Gotham's citizens, such as your parents. Gunned down by one of the very people they were trying to help. Create enough hunger and everyone becomes a criminal. Their deaths galvanized the city into saving itself, and Gotham has limped on ever since. We are back to finish the job.
In How the Grinch Stole Christmas!, the Grinch wants to remove the holiday from society because he finds the mindless joy, celebration, and materialism annoying (Type 3) and also because the singing hurts his ears (Type 2). In the live action film version, it's revealed that it's really a case of Type 4 - the Grinch subconsciously desires revenge for being ostracized as a child because of his odd appearance.
Ishamael has elements of this- he teamed up with the Dark One because he came to the conclusion that the endless repetion of The Wheel of Time made life pointless misery, and he decided to end it by simply breaking the Wheel (which would also have the effect of destroying the universe). He's also a Death Seeker, but is Genre Savvy to the fact that his cosmos runs on reincarnation, meaning that if he wants to kill himself, dragging the rest of reality down with him is the best way to make sure it sticks.
World of Ptavvs demonstrates this in its most basic form, with the last survivor of a telepathic alien race stranded on Earth and surrounded by humans, their unshielded minds boring into his. In fury, he blasts a powerful command: "STOP THINKING AT ME!" Quite a number of people do, and everyone else in the world is left dazed. This isn't a matter of lack of control, by the way—he views all non-telepaths much the way most humans view cattle, and if they must be sacrificed for his comfort, well, it's not like they're people like him. And the whole mess is solved by a Finger Poke of Doom. From one of the cattle.
The Wintersmith in the Discworld novel of the same name wants to win Tiffany's heart by saving people from their constant fear of death... forever.
Also in Guards, Guards when Vimes sees Sybil Ramkin's room the narration says something about how anyone witnessing it might be filled with a "diffuse compassion and decide that the best thing for everyone would be to wipe out the human race and start over again with amoebas".
Debatable example: Aurora claimed to be doing it for the sake of mortal humans who get caught up in the battles, she just failed to consider the consequences of disrupting the cycle of the seasons on earth.
Subverted in the New Jedi Order. Onimi, the real Big Bad, has a lengthy Motive Rant in which he describes to a captive Jaina Solo how horrible his life has been and how he's going to kill every living thing in the galaxy so he can become a god, all to get back at the gods he believes in, because he thinks they ruined his life (oh, and he also thinks Jaina is the avatar of one of these gods). The subversion comes because contrary to what Onimi thinks, rather than making him sympathetic, this rant just makes him come off as very, veryinsane.
One of many stories in The Name of the Wind is about legendary hero Lanre, who decides after the death of his wife that the world isn't worth living in any longer. For anyone.
Prince Gaynor the Damned of the Corum series by Michael Moorcock. Long ago, he was cursed with eternal life, and he joins the side of some Eldritch Abominations who are trying to plunge the world into an eternal winterland where everything will die—hence, he will finally achieve the death he yearns for.
The northern dragon in The Pilgrim's Regress is heard praying for God to destroy all the other creatures in the world so that he won't have to guard his nest.
Subverted in the fifth Spellsinger novel: a cosmic being is captured by a madman and its attempts to escape will eventually destroy the world. Clothahump assumes this is a grandiose suicide. It's not; Braglob is just too stupid and crazy to realize what'll happen.
Lord Foul in the Chronicles of Thomas Covenant is a type 2. He's a Cosmic Entity trapped within physical reality and linear time, and he wants to return to his natural state. Problem is, the Arch of Time is in his way, and to get out, he needs to destroy it. Destroying the Arch would, be extension, destroy the world. Being a God of Evil even before his imprisonment, Foul's not too fussed about the whole "destroying the world" part of the plan.
Live Action TV
Willow Rosenberg, in Season 6 of Buffy the Vampire Slayer. She attempted to destroy the world out of grief in the sixth season finale after her Roaring Rampage of Revenge over the death of Tara ended with a magical overload that briefly attuned her to the thoughts and feelings of everyone else on the planet. Overwhelmed by the world's collective pain, she decided that "your suffering has to end" and turned her newfound power towards bringing about The End of the World as We Know It. She was finally stopped by the The Power of Love.
A minor villain in the short-lived Birds of Prey series had the ability to mimic the abilities of other metahumans. Unfortunately, he was also an anti-meta bigot who had horrifying migraines whenever another metahuman was around. His motivation was thus a combination of Types II and III, in that his physical and emotional pain was caused by the presence of metahumans (to the point that he commits suicide in the end) and that he considered metas to be an abomination.
Exalted features the Neverborn, an example of Type 5. Once, they were Primordials, the creators of the universe, but as they designed it, they didn't believe the cycle of death would ever need to incorporate something as grand as themselves. So when they ended up getting killed, they found they couldn't pass into Lethe, eventually undergoing the cosmic equivalent of sepsis without ever being able to die from it. So they plotted to feed Creation into Oblivion, mainly so it'd stop the pain.
A few of their chosen soldiers, the Deathlords, are a mixture of Type 2 and Type 4. The Dowager of the Irreverent Vulgate in Unrent Veils, the Bishop of the Chalcedony Thurible, and Walker in Darkness all consider themselves priests of Oblivion, dedicated in bringing the peace of nonexistence to a suffering world. The others just want to Take Over the World to varying degrees.
The Delphi Organization from Trauma Center: Under the Knife, Under the Knife 2 for DS, and Second Opinion for Wii is an example of this. They believe that doctors are ruining the world by creating an inequality in society where the poor die and the rich get treatment. They believe the world would be better off without medicine and create a disease, GUILT, which will attack anyone without discrimination.
In Fable II, Lord Lucien became obsessed with the power of Old Kingdom technology after the death of his wife and daughter, which eventually drives him to reconstruct an Old Kingdom device known as The Spire, with slave labor, and use it to reshape the world to his liking. Oh, and along the way he murders your sister, along with countless others, including your wife and kids, if you have a family, and your canine companion.
Kuja in Final Fantasy IX, after learning that his lifespan is limited and will soon run out, throws a Suicidal Cosmic Temper Tantrum and decides to destroy the Crystal, the source of all life (think the spring from which The Lifestream flows) to wipe out all life on the planet. And why? Because he thinks it's unfair that life will go on and people will continue to exist after he's dead.
Played with in Sands of Destruction. Morte wantsKyrie to do this by showing how crappy the world is with the ferals' supremacy, hoping that he'll want to destroy it with his Destruct powers. He doesn't.
Ganondorf in Wind Waker wants to use the Triforce to take control of all of Hyrule and is willing to beat up two kids to get it. Just before attacking, he gives a very heartfelt monologue about how his people, who lived in a desert, were constantly dying while the rest of Hyrule prospered and how this made him want to control the land in which everyone lived a better life.
Os-Gabella in Fall from Heaven, the jaw-droppingly awesome dark fantasy mod of Civilization 4. She's hoping the destruction of Erebus will finally allow her to escape her pretty sucky everlasting life.
Professor Gerald from Sonic Adventure 2 initially seems to be a genocidal Mad Scientist, but once we learn that the cause of his insanity was losing his home, his research and his granddaughter, all that was important to him in rapid succesion, it's hard not to feel a bit sorry for him.
Shadow follows the same mold. Gerald's granddaughter, Maria, was his only friend. Seeing her killed by a group of humans changed him. 50 years later, he followed Eggman's plot for world domination, while fulfilling Gerald's goal of destroying it, believing that Maria also wants this. It's not until the plan is set in motion when he remembers that the granddaughter's dying wish to him was actually to save the world, not to destroy it. Shadow became a hero, or anti-hero in this case, since then.
Silent Hill: Claudia from the third game and Walter from the fourth certainly count, wanting to summon a Cosmic Horror they view as divine ("God" and "Mother" respectively) to cleanse the world of pain and loneliness.
Yggdrasill of Tales of Symphonia. He spends 4,000 years trying to bring back his dead sister, while trying to fulfill her last wish of a world without discrimination. Unfortunately, he ends up deciding that the best way to accomplish that is by creating a world of lifeless beings.
Sargeras the Fallen Titan became depressed and then omnicidal after fighting the endless evil forces of the universe for long enough, becoming convinced the universe was inherently flawed and would need to be destroyed so that it could be built anew.
Malygos from World of Warcraft wants to destroy the world because he doesn't like how mortals are using magic. His life sucked before he ultimately snapped. He was betrayed by his best friend Neltharion (aka Deathwing, who had been corrupted by the Old Gods), who then went on to wipe out almost all the other blue dragons, coming very very close to making Malygos the Last of His Kind. He later supposedly regained his sanity (after being exposed to some volatile magical energies from another planet). Um, yeah.
Purge from Space Channel 5 Part 2 could be considered this if you take the time to read the profiles for some of the Rhythm Robots and his own profile.
Wander, the player character in Shadow of the Colossus, needs to kill sixteen Colossi in order to revive Mono. Not because the Colossi were hurting anyone, mind; that's just what the ominous voices in the temple demand of him before they will help him.
The Big Bad of Arcanum, Kerghan, first of the necromancers, plans to kill every living thing in existance before allowing himself to die, because he died once already and discovered that the afterlife is a state of eternal peace, whereas life is pain and misery. He brought himself back from the dead in order to carry out his plan, claiming that people only fear death because they do not know the eternal bliss that lies beyond. Also, because living necromancers can summon the spirits of the dead back from the afterlife, so he himself cannot be certain that his eternal peace will not be disturbed by the living.
Takaya in Persona 3, like Kuja, is doomed to die young and plans to take the rest of the world with him. Both he and Ikutsuki believe that the world is too corrupt to be allowed to continue on.
In Shin Megami Tensei IV, the White are incredibly ancient spirits of despair, and decided the whole Order Versus ChaosForever War was entirely pointless, to the degree the world simply didn't deserve saving. By proxy, since Neutral endings are mere islands of stability between the larger conflicts, it also has to go. They created a machine whose destruction would trigger an Apocalypse How and do everything in their power to convince you reality is so horrible nothing short of a Mercy Kill can "save" it. And they can succeed.
The Big Bad of Radiant Historia essentially decided that since most people are selfish dicks who are more interested in short-term profit than actually trying to fix anything, awful people keep ending up in positions of power, the exceptions to the former keep getting killed by the latter for being inconvenient, and the only reason the entire continent hasn't disintegrated into sand yet is through a Heroic Sacrifice every few years by someone who has no real choice in the matter, the world doesn't deserve to be saved, especially if doing so would require him or his nephew to die. Cue Refusal of the Call and deliberately sabotaging the timeline to make the apocalypse as hard to prevent as possible.
Penny Arcade Adventures: The Brahe clan has, over the course of generations, discovered that their world goes through an endless cycle of destruction and rebirth, each time getting more horrific. By destroying the seeds by which it reforms itself, they hope to end the cycle and send everything to oblivion. Tycho Brahe (the most recent one, anyway) has an alternative plan: to seed its rebirth with a perfectly good individual — his niece, Anne-Claire. Also, the player character of the first two episodes is his backup.
Otani Yoshitsugu from Sengoku Basara is more a case of "Put them all in as much misery as me". His goal is to spread the same pain throughout the world as he suffers due to his leprosy.
Tavor from Looking for Group: After losing his family and kingdom to invaders, he decides to take his pain out on the rest of the world by trying to destroy the city/empire that abandoned them to the invaders, even if the city represents the world's last hope for justice and peace.
In one version of Butch R. Mann's psychopathy, he both sees himself as The Everyman, and deeply hates himself. He repeatedly chickens out of suicide, so he instead kills other people to metaphorically kill himself over and over again. If he could, he would kill everyone in the world, but he would then go even crazier with no one left to kill. (Given how wildly Butch's personality varies from strip to strip, this often doesn't apply at all.)
This seems to be Dr. Horrible's motivation for becoming a villain: he wants to topple the system and bring about some kind of vaguely defined social change. Or at least that was originally it; this desire becomes more and more of an afterthought as the plot progresses.
In Broken Saints, Big Bad Lear Dunham's entire Evil Plan can arguably be traced back to his despair after the passing of his wife. Whether the pain of his loss unhinged him somewhat or whether it drove him to become the humanitarian Determinator he was prior to losing hope, there is no denying that losing the love of his life had some part in Lear's motive to re-start human civilization.
In an episode of The Real Ghostbusters, "Ragnarok and Roll", a wealthy young man tries to do this because he got dumped by his girlfriend.
Bender: I'm so embarrassed. I wish everyone but me was dead.
Also played with in another episode where Bender launches a campaign against technology. Upon meeting up with the Planet Express Crew, his greeting wasn't meant to imply this trope, but Bender quickly realizes why they might think it was.
Bender: I've come to free you from your complicated lives! ...the "complicated" part, not the "lives" part.
Demona of Gargoyles has suffered a great deal at the hands of humanity across her centuries-long life, and this ultimately leads her to an attitude of genocidal insanity towards that species. She's never entirely unsympathetic, though, due to her tragic (almost Shakespeareanly-so) backstory. True, a lot of it was indirectly her own fault, but that just winds up making her more pitiable. In any event, she thinks she can end her pain only by wiping out the human race, making her a definite example of this trope.
Duke Nukem, the radioactive villain from Captain Planet (and not the action hero by the same name) wants to spread radiation because he draws strength from it and actually weakens when not getting a regular dose; he wants to turn the world into a radioactive paradise where he and his kind can live and thrive. Compare to the other eco-villains who are mostly motivated by greed or evulz.
Lilith, Adam's first wife (who does not appear in the Bible itself, but is present in several myths regardless) left Eden because she refused to be subservient to Adam. God decreed that for every day that she was gone, a hundred of her children would die. In retaliation, she is said to kill and eat human babies.