Perfection Is Impossible

A common motivation of villains is the perfectly understandable desire for a perfect world- one where their little sister wasn't murdered and people are all nice to each other, a world where everyone ascribes to their political philosophy. A work is usually set as they try to achieve it, with the protagonists opposing, or after their goals have had some measure of success, and the protagonist has to make others see how imperfect it is.

The reasons perfection is impossible are myriad -- existence becomes boring, people are chaotic and changing them is either impossible or requires fundamentally changing them, such as Instrumentality. The most basic reason is that everyone has a different perception or definition of "perfect".

Occasionally, even though the characters feel they have found perfection it may not jibe with what the audience would consider perfect, requiring euthanasia or some other societal taboo.

Sometimes the point will be made that while perfection is a worthy objective, it is an inherently unattainable one and any who claim to have found it are deluding themselves.

Related to Utopia Justifies the Means.

Anime and Manga
"Mayuri [to Szayel]: There is nothing in this world that is truly "perfect"... To true scientists like you and I, "Perfection" is tantamount to "despair". We aspire to reach greater levels of brilliance than ever before, but never, NEVER, to reach perfection. That is the paradox through which we scientists must struggle. Indeed, it is our duty to find pleasure in that struggle."
 * Bleach: In-Universe example between Mayuri and Szayell Aporro, who claims to be 'the perfect being'.

Film -- Live Action

 * Hugo Drax's fatal error in the James Bond film Moonraker; he uses Jaws as a henchman, but when Jaws realizes that he and his love interest will be disposed of as imperfect he helps Bond foil Drax's plan.
 * In Tron: Legacy, CLU was intended to create the perfect system. He turned the Grid into a Dystopia instead, and exterminated the miraculous ISOs because they were an imperfection.
 * This is the reason why Nina in Black Swan starts going through an emotional breakdown.
 * Hot Fuzz and the Neighbourhood Watch Alliance.
 * The machines in The Matrix tried to create a perfect simulation for the humans, but lost a lot of "crop".
 * Serenity showcases the horrible side effect of the Alliance trying to create utopia.

Literature

 * Nathaniel Hawthorne's The Birthmark, where a man grows obsessed with removing his wife's (small, rather cute) birthmark and rendering her "perfect", and ultimately kills her in the process.
 * In The Giver, the creators of the society sought to eliminate war and prejudice, among other things, but in the process they give up many freedoms, the ability to see color, and kill anyone that doesn't fit in.
 * In Harry Potter, Voldemort saw death as an imperfection. In trying to free himself from it he both brought it upon other people and destroyed his own soul, which over time made him lose what was important in living in the first place.
 * In Thief of Time, The Auditors create a female body for their agent. They mean to make her attractive but since they don't really understand the concept of beauty, they keep "improving" the original design, removing birthmarks and smoothing the skin and hair until she looks like porcelain doll that reeks of Uncanny Valley. Later it turns out that all their human bodies have another flaw - their senses are so perfect that any food that isn't completely bland kills them with sensory overload.
 * Judge Dee has a conversation with an artist he doesn't really like, telling him there's no point in perfection, as otherwise there'd be nothing left to do.

Live-Action TV

 * Babylon 5: The Ikarran civilization created living weapons programmed to destroy anything that wasn't "Pure Ikarran". None of them lived up to their own standards.
 * In Star Trek, the Borg are driven to assimilate more peoples and cultures so they can reach perfection (using all the best parts of each culture and their technology). Of course this leads to mercilessly killing, assimilating, and destroying civilizations.

Tabletop Games

 * Common in Dungeons & Dragons.
 * In Dragonlance, the attempt to create a perfect good world resulted in morally questionable attempts to get rid of evil, culminating in the Cataclysm.
 * Lawful factions in Planescape often commit major screwups in the name of perfection.
 * Also in Planescape, Baalzebul, the Lord of Maladomini, the Seventh Layer of Hell and the Lord of the Flies, was so named because he desired perfection right down to the smallest of flies in his realm. A Fallen Angel who was kicked out of Celestia for desiring unreasonable perfection, he has yearned for a city dedicated to his greatness for millennia, but his subjects can never build one that pleases him. Every time such a project is completed, he judges it unworthy and orders construction to begin anew, abandoning the failed project. Ironically, Baalzebul’s madness has caused Maladomini as a whole to become anything but perfect,  the formerly lush and fertile layer having become a blasted wasteland of decay and filth, the landscape covered strip mines, dead tree stumps, and factories that spew smoke and ask into the sky, along with hundreds of abandoned cities populated by deserters and squatters - he occasionally sends his armies into them to root them out, but they simply flee to another ruined city each time, having many to choose from. The Lord of the Flies can envision the perfect city in his head but cannot make it reality, and the same can be said of his political ambitions in Hell’s twisted hierarchy.
 * The Phyrexians in Magic: The Gathering created a society based upon seeking perfection (and on worshiping their power-mad leader). "Perfection" involves removing most human body parts and replacing them with machines and rotting zombie flesh, turning themselves into horrific zombie/cyborg patchwork abominations designed to be the "perfect" killing machines. Their sense of aesthetics is based solely on how efficiently any given "design" can kill things. Most non-Phyrexians are understandably horrified by the results.
 * In New Phyrexia, the White and the Blue Faction carry on this design in two different flavors.
 * In the Old World of Darkness game Changeling: The Dreaming, this was the whole problem of Nocker equipment. They were so dedicated to perfection that they would keep tweaking and tweaking only to have some tiny quirk or hiccough elude them.
 * In the Ravenloft setting, the dreaded artifact the  Timepiece of Klorr came about because the obsession of a clockmaker whom it was named after. He was obsessed with time, so obsessed that he struggled to control the one timepiece he could not set to perfect synchronization: his own heart. Research into dark magic and unspecified entities led him to create this pocket watch, which did indeed cause his heart to beat in perfect time, and also made him immortal, along with giving him access to several time-related powers (in game terms, the watch's spell-like abilities include Haste, Hold Person, and even Time Stop) but with a terrible price. The user must murder — not just kill — sentient beings to pay for this effect, or the watch takes his life, which is what presumably happened to its creator.

Video Games

 * In Telltale Games' Back to The Future adventure game series, this is what Hill Valley becomes after Marty inadvertently sets it up. People aren't killed, but a brainwashing program has just recently started (with Biff being the first victim, and Jennifer getting brainwashed later), and completely innocuous things like pinball, bubble gum, and even dogs are outlawed by the mastermind behind it all who likes none of those things. At one point, said mastermind uses Biff's reprogramming to force him to attack an unarmed man to steal surveillance tapes that show the unhappiness of most of the populace, just to prevent another powerful character from seeing said tapes.
 * StarCraft: Like the Borg, the Zerg are dedicated to the pursuit of genetic perfection by assimilating the dna of the most advanced species in the galaxy, their end goal being the Protoss (with humans as an afterthought). Upon the overmind's death, Kerrigan took up the mantle as the more literal Hive Queen and became more liberal on what the Zerg could assimilate.

Web Comics

 * Sluggy Freelance's 4U city showed an attempt at Utopia derailed by the technology behind it Gone Horribly Wrong.

Web Original

 * In Sailor Nothing, this is the background of the entire Yami-Gaia; a priestess tried to purify herself of corruption, but instead gave it physical form as the Queen.

Western Animation

 * Avatar: The Last Airbender: Azula is an interesting example. For a time, it seems that she is absolutely perfect and unbeatable. However, the minute her friends Mai and Ty Lee turned against her, she starts to have the mother of all Villainous Breakdowns.
 * In the Captain Caveman segment of The Flintstone Kids, the hero started competing with a new hero called Perfect Man. Being a classic Flying Brick, Perfect Man actually seemed to be a much better crime fighter than Captain Caveman, so the older hero considered retiring. Unfortunately, once Perfect Man got rid of all the crime in Bedrock, he took things too far and started running the place, changing the rules the way he thought they should be, figuring that's the way they should be because, well, he was perfect. Captain Caveman couldn't defeat him with brawn, but did so by proving he was not perfect: he told Perfect Man that if he truly was perfect, everyone would like him, and it was clear now that everyone hated his guts. This revelation sent Perfect Man into a major Villainous Breakdown, and he gave up without a fight.

Real Life

 * Among the many parts of the US Constitution that make it impressive is the phrase "to from a more perfect union". Not perfect, more perfect, setting an actually attainable goal.
 * Logic, quite rigorously, in the form of Godel's Incompleteness Theorems. Logical systems are constructed to be able to prove all true statements and no false statements. Instead, Godel proved that any system that proves all true statements must also prove at least one false statement - and if the system is fixed to eliminate false statements, it stops being able to prove at least one true statement. It's a dilemma between completeness (all truth) and consistency (only truth). Or being unable to do arithmetic.