Villains who can actually serve very important purposes and need to be kept alive despite their evil deeds. No matter how sadistic, bloodthirsty, cruel, or even how much they are hated, these villains have to live or something terrible will happen. However, a) once they fulfilled their purposes or if there is a good / less evil alternative and b) they still choose not to redeem themselves, whether they get killed off or suffer a demise no longer matters, as they are no longer needed at that point and still have technically done evil things.

These characters are similar to Virtually Resourceful characters, but are obviously opposed to their alignment. Also, these characters are usually created to keep the story relatively three-dimensional.

Notes about Pure Evil villains

Pure Evil villains CAN be necessary, regardless of how wicked they are. Despite being very evil in the setting in which they appear, their status, power, or occupation may be necessary to uphold the order of the place that the story takes place in, thus they are, in a way, "Necessary Evil." Technically, this includes Purely Evil villains who fall under the first, fifth (in circumstances like these, it is considered Evil Vs. Evil), third, sixth, twelfth, or twenty-first criteria - and ONLY these criteria.

This is not a redeeming quality, as the Pure Evil villain is still dangerous to the setting that they happen to be necessary in. For example, abusing or enslaving those around them while upholding stability to something greater that they are apart of. Akainu from One Piece is a powerhouse that is needed to stop the pirates. But while he is needed for stopping dangerous pirates, he is a purely evil individual who is abusive of his power. Nevertheless, keep in mind that adding a Pure Evil under Necessary Evil MUST remain exceptional.

In another extreme case, there are Pure Evil villains that can still be necessary to the story itself from where they came from. This happens only when the villain is the "key" character to the work from where they came from. In other words, "without the villain, there is no plot". For example: Isaac Ray Peram Westcott from Date A Live is the catalyst character from the series. Without him, the universe of the said work would have never existed to begin with as it was him who set the events of the story in motion by summoning the Mio Takamiya on Earth, starting the story in-universe. As such, the same villain killed the main protagonist of the series (when he was an ordinary citizen), Shinji Takamiya, and so restarting the life of the hero and giving birth to the main protagonist of the series. Later in the story, the said protagonist would be the saver of the universe, stopping Westcott's ambitions. Aside from that, Westcott's Deus.Ex.Machina Industries is necessary to the world as they provide weapons and power to all nations. Without DEM, billions will suffer from a global economic crisis. Other examples of this are:

• Frieza from Dragon Ball Z: who destroyed the Planet of the Saiyans, resulting in the main hero of the story, Son Goku, being sent to Earth, where he would grow into one of the universe's greatest defenders. 
• Lord Embryo from CROSS ANGE Rondo of Angel and Dragon: the lustful god who destroyed many Earths in the past and created the world where the series take place. Without Embryo, the main protagonist of the series, Angelise Ikaruga Misurugi, would never have been born as a Norma and so becoming the universe's protector.
• Makuta Teridax from BIONICLE: The Makuta once served as the protector of the Matoran as well as the trusted commander of Miserix before attempting to overthrow the Great Spirit. Without Teridax, the Matoran Universe would have been attacked by the other villains.

Villains who qualify

Villains who fall under at least one criteria are Necessary Evil:

1. Some anti-villains with the intent to help the hero or to save a large number of people. Often, these characters are considered anti-heroes (a noteworthy example is The Punisher, while being a violent vigilante, fights off and defeats various supervillains).
2. Villains who are keeping a much worse evil at bay (e.g. Galactus keeps Abraxas, a being able to destroy entire universes, out of the Marvel Universe; Anna Morgan, whilst depicted as an abusive and mentally disturbed mother, keeps her adoptive daughter Samara Morgan from continuing her torment and killing spree).
3. Jerk employees and employers that actually are capable of doing their jobs and it's made very clear the business cannot succeed without them (e.g. Benson is heavily trusted with keeping the park afloat; Malcolm Tucker was very capable in doing his job as the Director of Communications).
4. Villains preventing catastrophes, including the end of the world or universe, with their mere presence or actions (e.g. Kyubey prevents Armageddon with energy collected from magic girls).
5. Evil vs. Evil scenarios where one of the villains is the only subject strong/powerful enough to defeat the more dangerous threat (e.g. Lord Garmadon was the only person who could wield all four golden weapons to destroy the Great Devourer; Stewie Griffin was the only one who could stop Diane Simmons from killing Lois; Heinz Doofenshmirtz was the only person to stop Aloyse Von Roddenstein from creating a new Ice Age).
6. Unlawful businessmen that can provide a product or service that is needed or well-liked by people (e.g. Mr. Krabs runs the Krusty Krab which produces the very well-accepted Krabby Patty; Seto Kaiba is in charge of KaibaCorp). This can also apply to entertainers who perform or create to please and entertain people (e.g. Misa Amane).
7. Villains performing villainous acts that lead to beneficial results/consequences, whether the result itself was what they intended or otherwise. Some cases of this instance show where villains whom their actions was turned out only to merely trained/molded the heroes so the said heroes can become a better savior (in which they often revealed in the end). Other cases, however, show that either their actions are the key for their future downfall at hands of heroes that they antagonize or made hero realized the grave situation that everyone faced (e.g. Mister Babadook made Amelia comes to terms with her husband's death; Joe Chill murdering Martha and Thomas Wayne leads to Bruce Wayne becoming Batman; The Architect created the One prophecy for Neo and his predecessors).
8. Wealthy villains that helped the city they live in (e.g. Mr. Burns is Springfield's only taxpayer, and Lex Luthor, who employs most of Metropolis' workforce.)
9. Amoral entities that must keep the balance of nature in check (e.g. most incarnations of the Grim Reaper).
10. Family breadwinners (e.g. Peter Griffin, while being a dimwitted arrogant that causes many problems to his relatives, is often the only person in the family who actually works to put food on the table).
11. Villains with important informations that are necessary for the heroes and the other characters to either save people or defeat more dangerous evil-doers. (Hannibal Lecter had information that helped Clarice defeat Buffalo Bill.)
12. Some heroes who turned to the dark side that had everything related to their evil actions upon their fall from grace exposed, would led to undesirable consequences (e.g. when Harvey Dent helped locked half of Gotham's crime bosses away in The Dark Knight, he gave hope to Gotham; but when he became Two-Face and started killing people, Gordon and Batman knew if the truth came out, people would lose hope so Batman willingly took the blame so Dent would stay a hero after his death).
13. Villains from the Lawful Neutral alignment who keep order, and it's obvious that situation would be worse had they not been present (e.g. Razoul, despite being amoral and corrupt, keep peace and order in their home cities).
14. Hostile biological species, tribes, or civilizations that, while hostile or xenophobic, are capable of producing children and families. Killing of a naturally hostile race, civilization or tribe would still be considered an act of genocide (e.g. the Yuuzhan Vong, The Grox, and the Predators).
15. Evil teachers who keep unruly students in line.
16. Alter-Egos or powerful entities within a hero, the ones that has possessed the hero, or grant them their powers, resulting in them saving his/her lives from time to time (e.g. Zangetsu possessed Ichigo multiple times and, as a result, saved his life multiple times; Kurama sometimes possesses Naruto or gives some of his power to prevent Naruto from getting killed or to fight off a powerful foe).
17. Former villains that joined, or at the very least, helped the heroes (e.g. Yasha, Trish, Bagramon when he was the Old Clock Shop Man, and many others).
18. Villains who saved a protagonist(s), attempt to sacrifice themselves to save a protagonist(s), or sacrificed their lives to save the protagonist(s), such as SA-X, Sybok from Star Trek V: The Final Frontier; Android 16 who attempted to self-destruct to kill Cell; and questionably Nemesis from Resident Evil: Apocalypse.
19. Double agents that are on the side of good and pretend to be evil. These people can be either friends of the heroes whom originally at odds with heroes but ultimately chooses to switch side with the heroes and leaked the antagonists' evil scheme on them. (A famous example is Severus Snape, who pretended to be allies with Lord Voldemort and his forces but was secretly helping Dumbledore and Harry Potter).
20. Dark Forms, Devils, Gods of Evil or other personifications of evil that are literally the source of evil. If they are destroyed, evil would cease to exist, and life would no longer be able to feel sadness, anger, or any other negative or evil emption and be forced to feel positive all the time, be incapable of doing anything evil or neagative, and think that negativity is unnatural. So villains who are the source of evil have to be kept despite their evil influence.
21. In video games, certain evil creatures such as the hostile mobs from Minecraft, that can be farmed for useful items (killing a Wither will give you a Nether star, which is the key ingrediant to make a beacon, killing an Evoker will give you a Totem Of Undying, which prevents you from dying, Blazes can be farmed for their rods to power your brewing stand(s), the Ender Dragon can be re-spawned to collect Ender Acid to make lingering potions, and so on).

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