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Love to Hate
This villain trope is for people we love to hate.
"Love to hate" is a term we (and others) use to describe villains we enjoy. We love them for various reasons, such as excellent character development, being hilarious, possessing the best writing, having a memorable personality, or were lucky enough to have a top notch performance by their actor. (Of course, the fans still want to see the wretch get his comeuppance in the end, hopefully with a flamboyant Villainous Breakdown and delicious Humiliation Conga sequence. This is still hatred, after all.) Also named Heel Hate.
Faux Affably Evil, Affably Evil, Laughably Evil, Magnificent Bastard, and Card-Carrying Villain are sub tropes for different reasons. Being a Large Ham definitely helps (see also Evil Is Hammy). An Anti-Villain is often one of these due to the character development they often get. A villain who is The Smug Snake, The Scrappy, and Creator's Pet, is typically not eligible for this trope as are some villains who cross the Moral Event Horizon or qualify for Complete Monster.
Do not confuse with Draco in Leather Pants, which is when a villains' fandom is over-eager to gloss over the actual nastiness of a villain and insist that he or she is just misunderstood. Also not to be confused with when the heroeswould love to hate the villain, but just can't manage it.
This is someone whom the fans enjoy and even maybe respect because of their unapologetic evilness. Their shamelessness is cathartic to us, and they retain their awesomeness as time goes by without Villain Decay.
In order to be eligible, a villain must be generally well regarded/well liked by said fandom while the same fandom still acknowledges they're a villain (again, if the fandom instead likes the villain so much that they want to falsely claim the character isn't a villain, it's not this trope but rather Draco in Leather Pants instead). Being here means that said villain is part of the pantheon of great villains.
While most of the major villains in Dragon Ball Z have their share of fans, Cell is easily the most popular, largely due to the fact that for much of his arc, he shares the Saiyans' love of a good fight, and the search for one. He's also much more Affably Evil than Freeza, and less of a Complete Monster that Majin Buu's later incarnations turn out to be.
Sir Crocodile, Arlong, Eneru, and Spandam as well. All of them unrepentantly evil but all so entertaining because of it.
Digimon: Myotismon was far and away the record-holder for the most evil villain, until Kurata topped him by far. Both characters seem to be treated like the Joker in fandom - people can't get enough of talking about how so sick and twisted they are, but it's definitely love... compare to the treatment of anyone in the way of a popular pairing.
All factors seem to indicate that DecilGalette of Gundam AGE is also heading in this direction.
Agon from Eyeshield 21 is this to parts of the fandom. He's just such an over-the-top depiction of a jerk jock (with absolutely no traces of a Freudian Excuse to justify it), that even those who despise the character will agree that the series was at it's emotional best when Agon was the main antagonist.
Team Rocket in the Pokémon Best Wishes series. The recurring trioTook A Level In Bad Ass and are now more straightforward villains who rarely show the silliness or softer side they used to flaunt, and are thus easier to dislike. Yet they still keep the flamboyant style, overconfidence, and eccentric motto recitals that they built their career on, which makes (most of) the audience love it when they're on-screen.
Marik/Dark Marik from the Battle City arc. While Marik was pure Mr. Fanservice despite the acts he committed, Dark Marik was so twisted and Axe Crazy that we can't forget him.
Dartz from season 4. He's pretty much the most evil villain ever, considering the things he's done compared to the other villains, and that was a Filler Arc!
Envy is this for the saner contingent of the fanbase (those who don't try to put him in leather pants), since it's easy to see him as cool, yet still despise him not only for killing Maes Hughes, but for starting the Ishvalan War. Then there's Pride for being a Creepy Child and The Dragon to Father, not to mention how unsettling he is.
Fate/zero has Bluebeard, whose seiyuu shows the talent for the dramatique. Meanwhile, Fate/stay night has Kirei, who does Evil just-because, making a nice Foil for Shirou who does Good just-because. Of course, both has their arses kicked with much gusto.
Bluebeard and his master actually discuss this trope in-universe. Ryuunosuke claims that in his world-view, God is a playwright writing the greatest tale known to man and thus loves all of his characters no matter how wicked they are; after all, what good is a tale without a villain? Bluebeard embraces this vision and decides that the pair shall honour God by performing an act of villainy unmatched so far in Creation.
Loki of Thor. Gotta love the brotherly hate they feel towards each other, but gotta hate his attitude and his complete monsteriness.
Up until he died and came back as a mischievous, pre-teen Magnificent Bastard. It's only a matter of time until his inevitable turn back to evil, but right now he's all love.
In Harry Potter, Dolores Umbridge is an interesting example. There are eviller villains in the series, to be sure, but none of them are quite so passive-aggressive about it, nor are many of them the type of people readers might actually encounter in real life. As a result, Umbridge is more fun to hate even than the Big Bad.
Bellatrix may be a better example, because she actually has enjoyable qualities as a character - she is bad-ass, sexy, hopelessly insane, and her actress gives a deliciously over-the-top performance in the movies. By contrast, Umbridge's character mostly exists to be a Hate Sink.
Voldemort himself arguably qualifies, seeing how he was voted the #1 villain in a poll that decided which character was the best literary villain.
Venandekatra the Vile from the Belisarius Series can be like this despite being a Complete Monster. Just the sheer effort of cramming so much evil and vice into the same character is amazing.
And Faith, and the Trio, and Holtz, and Lilah Morgan...Joss Whedon is just so good at creating villains who fit this trope!
Sylar, also pre-Badass Decay. Watching him trap and trick people was way more fun than it should have been.
Alfred Bester from Babylon 5 may have not been the Big Bad of the entire series, but you knew he was up to no good any time he was around - and it would always be awesome.
Davros as well. There's a reason even casual fans know his "to hold in my hand" speech.
The Daleks.
Another good one from the BBC is Madame President Servalan. Dear God, she usually walked away with whatever she was after and made the alleged heroes look like idiots in the process. Totally evil, but you can't help but admire her sense of style.
Brainiac recieves similar treatment. He's utterly cold and never shows a hint of emotion or remorse. And that's why the fans love him. Brainiac brought back Pure Evil to Smallville at a time when it was drowning in Lex's Wangst and it's what he's beloved for. James Marsterssnarky performance helped.
Sue Sylvester from Gleeis so petty and nasty and just so entertaining.
Music
Ice Cube claimed to be "The Nigga Ya Love To Hate" on his debut album AmeriKKKa's Most Wanted, because of the firestorm of controversy surrounding him at the time.
Yuna from Breath of Fire IV game can arguably be counted, as well. Despite being an outstanding Complete Monster and a Smug Snake, he is considered to be one of the best villains in the series by most of the fandom.
Eliphas the Inheritor and Gorgutz in Dawn of War. The former for his dark charisma and wit, the later for laughs.
Eliphas is coming back for Dawn of War 2: Chaos Rising. There was much celebration amongst the fans.
Now we just need Gorgutz to make an appearance, and we'll have a winner.
Apparently Gorgutz was killed off in a side-comic some time ago. Unless it was just another warboss with the same name. To be far his death was pretty funny: he got crushed by a Gargant's flying head.
Skyward Sword has Ghirahim, the camp but creepy villain who's become very popular with fans. And while not necessarily a villain, Groose was loved for being a hilarious Large Ham even before he stopped being a jerk to Link.
Dr. Eggman/Robotnik from Sonic the Hedgehog. A rare case of Villain Decay actually making him more popular (due to being more sympathetic). Contrast with Eggman Nega.
Also Mephiles the Dark, one of the few redeeming things about the 2006 game.
Most villains from the Metal Gear Solid series except Volgin. Many of those examples are also Anti Villains themselves.
A rare exception to the Smug Snake not being eligible is Zetta from Makai Kingdom. Hilarious to watch, and intentionally done to be a parody of the Smug Snake.
Lezard Valeth of Valkyrie Profile. Somewhat problematic because half of his fanbase is in the Draco in Leather Pants camp, but even those that find him abhorrent believe the series wouldn't be half as good without him.
Dracula from the Castlevania series, who just continuously keeps coming back, just to get killed and then revive and then get killed and, you get the picture...
Erol from the Jak and Daxter series, who is a colossal Jerkass to Jak from the second his character is first introduced to just before he blows himself up. As if that isn't enough, he comes back from the dead in the third game and takes over the position of Big Bad.
General Sarrano from Bulletstorm, a foul-mouthed Complete Monster who taunts and swears nonstop at the player until you are FINALLY able to kill him at the end of the game...or so you think.
SHODAN and SHODAN's speeches are essentially the main draw of the System Shock series. No other villain makes their taunting feel so bizarrely immediate, or so strangely personal.
BlazBlue: Both Hazama and Relius Clover exude this trope to the max. Hate their depravities, but admire their awesomeness while doing so, making them really solid villains to the series.
Dragon Age Origins gives us Rendon Howe and Loghain Mac Tir. In contrast to the incoherently violent, Always Chaotic EvilBig Bad of the game, Howe and Loghain had identifiable intelligences, with dialog that provided players heightened impetus. The battle with the Archdemon has inevitability beyond the need for motivation, but the confrontation with Loghain is character-driven, and approaches with increasing dramatic tension.
More than anyone else in Saints Row 2, Shogo Akuji, leader of the Ronin, so much that his fate goes unpitied, and makes Ax Crazy Johnny look reasonable. And almost as hated is Maero's girlfriend Jessica. Perhaps the comparison to these two makes the Big Bad look a little more sympathetic; by the time of his confrontation, the player's character has generated a little of this trope on himself/herself.
Nearly any villain from the Ace Attorney series. Each villain is thoroughly explored and wonderfully played. For me, the best was Matt Engarde. He drove a woman to suicide, had a man assassinated, and had Maya Fey kidnapped as bargaining chip, at which point she was nearly starved to death. Why? To preserve his image. He also manages to sneak a glass of bourbon into the detention center. Not to mention that his reveal to Phoenix Wright was top notch, and the fact that he taunts you about Maya's capture makes him all the better.
Ridley from Metroid, beloved for his design, which is badass to the hilt, and for his apparent Joker Immunity, as well as the Awesome Music that tends to accompany his fights.
Pretty much all evil organizations in the Pokémon series. Especially hateable are Team Rocket, Cipher, and Team Plasma.
Saren Arterius from Mass Effect and, once finally revealed, hisboss. Few villains are as effortlessly terrifying. KaiLeng from Mass Effect 3 is paradoxically both hated and loved for being 1) a huge douche and 2) extremely gratifying to kill.
The Thalmor from "Skyrim". Almost literally Nazi Elves, the fans adore massacring any Thalmor patrols they see on the road for a variety of reasons, not limited to their smugness, various acts of dickery, and complete openness about trying to kill or enslave anyone who opposes or looks directly at them. Hell, they get more hate then any of the series' heralds of the apocalypse!
Miko's fall from grace turned her from simply Scrappy to this. When she killed the Cool Old Guy, the hatred she'd garnered up to that point reached critical mass, in-universe and out.
Clio Gabriella of Survival of the Fittest, full stop. This is a girl who relishes her kills. Yet to quote one of the members of the site:
Clio is an absolute bitch who will eventually get what's coming to her. But, you know, Clio could easily be a character that I actually WOULD hate just on principle alone, were it not for how she was written.
This did not however stop some members of the site being incredibly happy to see her go when she eventually bit the dust.
The Federal Epidemic Containment Agency (FECA) from the live zombie game/event Dead Town. Within the narrative, FECA agents routinely shoot at the protagonists, even calling air strikes on them and more the less ignoring zombies to instead attack the heroes. The Dead Town creators told me that FECA merchandise is the most popular they sell. I have a button with a cartoon man in a gasmask that reads, "FECA: We're Here To Help." Even though FECA did not help me when I played Dead Town! They're fun to hate!
Western Animation
The Joker is already this, but Mark Hamill's performance made him even more lovable... while being as monstrous as ever.
With Beast Wars, the case could be made for Tarantulus as well, especially once they start playing up the mad scientist bit in later episodes.
Tarantulus:(getting the drop on Dinobot and Rattrap) DIEEE, MAXIMALS!
Dinobot and Rattrap:(look over from their bickering) SHUUUT UP! (WHAM)
Transformers Animated Megatron is working on it. He's definitely recognized as an example of Took a Level in Badass (as compared to Megatrons past) but it remains to be seen if he'll be loved and remembered for years to come the way Beast Megatron is.
AnimatedStarscream certainly qualifies. Hilarious and sometimes very deadly, the guy steals pretty much every scene he appears in.
Transformers Prime Megatron looks to be running for most threatening and psychotic Megatron to date. His sadistic tendencies, brutal methods of engagement and overall creepy voice brings out his inner-monster to many.
Skeletor from the original He-Man animated series is fondly remembered as someone we loved to hate.
From the same creator, the Green Goblin/Norman Osborn, Doctor Octopus, Venom and Tombstone (who comes off as almost the unholy offspring of Slade and Xanatos) - four major villains from The Spectacular Spider-Man.
Osmosis Jones: Thrax a.k.a. The Red Death - one of the deadliest and coolest germs out there.
South Park: Eric Cartman (after crossing the Moral Event Horizon). Most of time he's just so utterly despicable that you just want to punch in the face, repeatedly. (So it was extremely satisfactory when Wendy did exactly that at some point) However, if you remove him from the show, it suddenly becomes a lot less funny. He's a Complete Monster, but an amusing one nonetheless.
Galaxy Rangers: The Queen of the Crown - you don't often see a villainess with that kind of leverage over The Hero. Nor are eighties cartoon foes that creative with Mind Rape.
Being the thinly-veiled expy of Q (complete with sharing the same actor) went a long way to making him this and earning him the Fan NicknameDisQord
Nightmare Moon also has her share of followers, being the Superpowered Evil Side of an arguablyBadass Princess. Of course, since her plan was to bring The Night That Never Ends (and in order to achieve this she was willing to kill members of the main cast) she's not exactly a lovable little angel.
Skullmaster of Mighty Max was an incredibly powerful, threatening and dangerous villain who threatened to eat a child's heart in the opening scene of the first episode, but with the voice of Tim Curry there's no way not to love this hateful monster. The fact that he never suffers Villain Decay, but instead becomes significantly more threatening as the show progresses only sweetens the deal.