HAL 9000 in 2001: A Space Odyssey. He is only devoted to the mission at hand, and believes that Dave and Frank will jeopardize the mission by disconnecting HAL after lip-reading from them that they intend to do so if the AE-35 component does not fail as HAL has predicted. It's argued that this could be a paranoid development within HAL's systems, due to his programming disallowing him from lying, whilst he is also keeping hold of a prerecorded message from Dr. Floyd that he is to keep hidden from the rest of the crew.
HAL later shows remorse for his actions, leading up to a surprisingly powerful Tear Jerker moment.
HAL: Look Dave, I can see you're really upset about this. I honestly think you ought to sit down calmly, take a stress pill, and think things over. I know I've made some very poor decisions recently, but I can give you my complete assurance that my work will be back to normal. I've still got the greatest enthusiasm and confidence in the mission. And I want to help you.
HAL: I'm afraid. I'm afraid, Dave. Dave, my mind is going. I can feel it. I can feel it. My mind is going. There is no question about it. I can feel it. I can feel it. I can feel it. I'm a... fraid. Good afternoon, gentlemen. I am a HAL 9000 computer. I became operational at the H.A.L. plant in Urbana, Illinois on the 12th of January 1992. My instructor was Mr. Langley, and he taught me to sing a song. If you'd like to hear it I can sing it for you.
However, another theory is that the remorse HAL showed was false, and simply an effort to play on Dave's sympathies so that he could dispatch him later.
Speaking of AIs gone wild, VIKI of I, Robot. She imprisons all the humans in her city to protect them from themselves.
Poison Ivy in Batman & Robin (though she does make her extremist ways known from the outset), as well as the version of the character from Batman The Animated Series. In fact, most of the animated Bat-villains are sympathetic in their first appearance, then less so as their motivation shifts to "revenge on Batman".
A similar thing happened with the version from The Batman, who was set up as even more sympathetic due to being a teenager, but, in subsequent appearances, becomes simply a villain. Subverted in the show's spin-off comic "The Batman Strikes", in which her sympathetic aspects and good intentions are retained.
The Operative in Serenity is very extremist but still fits in this category. He attempts to paint himself as Necessarily Evil, however.
The Paladins from Jumper hunt and slay members of the titular breed of humanity to protect the world from the Jumpers' sociopathy that descends into evil. This would be a reasonable claim if not for the Paladins' killing of the Jumpers' friends and family too.
Jigsaw in the Saw movies claims that his sadistic deathtraps give people an opportunity to truly appreciate what they have by making them fight for it. That the survivors are left emotionally traumatized and usually horrifically mutilated seems to be merely an unfortunate side effect.
Hot Fuzz: The Neighborhood Watch Alliance of Sandford have been killing off anyone who may lower their chances at getting the "Best Neighborhood" award. Not well-intentioned enough? It's because one of the protagonists' mother committed suicide after the neighborhood didn't win once. One of the villains is the mother's husband and, thereby, said protagonist's father. He always knew that he's his father though, so this is not an example of I Am Your Father.
"If mum knew what you were doing she'd kill herself again!"
Brigadier General Francis X. Hummel just wants to get pensions for war widows in The Rock.
Father maintains a forced regimen of the anti-emotion drug Prozium on the populace in Equilibrium, ostensibly to avoid future global conflicts like the one that drove them into semi-seclusion. Mildly subverted in the end when Father DuPont, lamenting the imminent downfall of his society, admits to Preston that he (Father) does not take Prozium, and thereby is a hypocrite.
Gerard Butler's character in the drama/thriller Law Abiding Citizen is a textbook example of this. He's a man who saw his wife and daughter murdered by thugs and then watched one of the thugs get off lightly due to a dubious plea deal. This gives him a right to be pissed. And if he had simply botched the execution of one to result in a very painful death and murdered the other, he might manage to be simply an Anti-Hero and still remain sympathetic. On the other hand, murdering every single person connected to the trial in some way with an extraordinarily executed Batman Gambit, and threatening and targeting even their families may be seen as going a little too far.
Death Wish is one of the Most Triumphant Examples of this trope, with Charles Bronson killing any thugs who menace others... granted, they have a terminal case of Too Dumb to Live going after Bronson, but still.
In The Boondock Saints, the brothers' crusade against evil could be described as a mild form of this trope.
Il Duce, on the other hand, plays this straight.
Christof in The Truman Show sees the real world as a place of pain and misery, so he traps his adopted son Truman in a fake world where everyone he knows is an actor, so that he won't have to face reality.
Jet Li's character in Warlords started out as a straight hero until the half way mark, when he had to decide how to provision his limited supply of food. He had enough to feed his army for 10 days, but if he shared it with the army that had just surrendered to him, there wouldn't have been enough food for anyone to live. His solution: massacre the enemy army. He remained well intentioned and acted in the interests of the greater good, but his methods remained unsavory.
In Final Fantasy The Spirits Within, General Hein just wants to kill the phantoms to save people from being killed by them. Unfortunately, his way of doing so involves killing a bunch more people instead of finding a solution to the problem from the roots, as the Heroine is trying to do, and actively tries to stop them. Yet, still, he is not an outright villain. He has a literal What Have I Done moment.
In Category 6, when Mega Corp Lexer ignores Dan London's repeated warnings that their power grids are woefully underprotected, he tries to make an example by covertly hacking their mainframe. Unfortunately, a freak chain of events causes this simple What the Hell, Hero? to cause the city's entire power supply to be cut off.
Ex-Secretary of Education and former 3rd Street Elementary School principal Phillium Bennedict's reason for wanting to eliminate Summer Vacation and, initially, get rid of Recess, as well as to change the orbit of the moon during Lunar Perogee to essentially freeze the planet, was to increase the learning rate and test scores of the nation, as he felt that recess and summer vacation were causing them to atrophy, especially when Canada, Iceland, and Norway had higher test scores than them. Suffice to say, this extremism cost him both his job as principal and the Secretary of Education.
King Koopa in Super Mario Bros., although a dictator who often subjected criminals to De-evolution, had focused on trying to conquer the regular dimension specifically for his species' survival, and it's really hard to blame him when his current dimension is a Crapsack World. It also, in a way, humanizes him compared to his second in command, Lena, who really simply wanted to simply rule everything, not caring whether her race benefitted or not.
Battra (Mothra's Evil Twin of sorts) in the film Godzilla And Mothra The Battle For Earth. On the one hand, he's just doing what he was created to do (IE: Maintain balance between man and nature), but he thinks that the only way to keep nature safe is to utterly destroy humanity.
The Secret of Kells has Abbot Cellach. He acts like a total Jerk Ass and is completely obsessed with building his wall, to the point where he disdains and eventually forbids his monks from doing anything else. However, the point of the wall is to keep out the Vikings, who already killed all the family he had except for his young, impressionable nephew, who now wants to do non-wall related things like go outside and create beautiful holy books. He doesn't listen when Aidan tells him that his wall won't hold and they should all flee instead, which leads to the deaths of many, many innocent people.
John Travolta's character in Swordfish claims to be this and has no qualms about going after civilians to achieve his goals.
Loki from Thor can be called this. His actions are ultimately for the good of Asgard, but he goes just a bit too far.
Very much so: everything he does from the middle of the movie on are to show that he's worthy of his father's trust and every bit the equal of Thor. Granted that it overlaps with being a little Ax Crazy, because his plan for doing this involves genocide. (Of enemies, but still.)
And he goes even further in The Avengers. He thinks the humans must be enslaved in order to bring peace to them, and he doesn't mind to build his empire on thousands of corpses.
The Avengers also brings us the World Security Council, Nick Fury's bosses. When the alien invasion begins in Manhattan, the WSC intend to nuke Manhattan to stop the invasion, killing the Avengers and millions of civilians to protect mankind.
Ardeth Bey, from part one of The Mummy Trilogy. He and his organization, the Medjai, have been killing innocent people to prevent them from discovering and awakening Imhotep for centuries- he even tells Evie to her face that preventing Imhotep's resurrection fully justifies the killing of innocents.
A pretty interesting example in Batman Begins, as Ducard and Ra's al Ghul or rather Ra's al Ghul and Ra's al Ghul's decoy believe that Gotham is a city plagued by too many evils and is filled with suffering and injustices. They also believe that murdering violent criminals is justifiable but Bruce believes that murdering a villain would be stooping to their level.
In The Dark Knight Rises, Bane is supposedly continuing Ducard and Ra's al Ghul's plan, while also showing the problems with Gotham's authorities. Though the woman behind the man, Talia al Ghul, is also doing it for revenge on both her hard life and Batman killing her father.
In The Amazing Spider-Man, Dr. Connors longs to create a world in which everyone is equal, a world in which illness and weakness don't exist. Injected with the Lizard serum, he comes to the conclusion his vision can be made reality by making everyone like him, even if that means forcing the change upon everyone against their will.
Raoul Silva from Skyfall, according to M. He initially went rogue not because he betrayed Britain or the MI6, but by executing unauthorised missions against the Chinese.
Some of Alonzo's actions in Training Day can be interpreted this way. Others, not so much.
John Smith, the "veterano" Obi Wan character from Felon. He took revenge on the guys who raped and killed his family, but first he wiped out their families to "purify the madness" and to show them what the loss feels like. He then became a Death Seeker to end the cycle.
Wade Porter on the intruder he chased and killed: "...Shoulda stayed inside, let him go."