"The road to hell is paved with good intentions."—Bernard of Clairvaux
"Fanaticism consists in redoubling your effort when you have forgotten your aim."—George Santayana
A villain who has an overall goal which the heroes can appreciate in principle, but whose methods of pursuing said goal (such as mass murder) are problematic; despite any sympathy they may have with his cause, the heroes have no choice but to stop him. Taken to extremes, he may fully believe that Utopia Justifies the Means. Such an idealistic extremist is likely to be either a Totalitarian Utilitarian or a Principles Zealot, depending on whether he's aiming For Happiness or For Great Justice. The most well-written examples of this trope are the kind that the reader/viewer stops just short of agreeing with.
Other times, the villain may be out for simple Revenge against a person or corporation or other entity that has undeniably wronged him. Again, the heroes may sympathize with his plight, but are obliged to stop him because he cares not who gets in the way of his planned revenge. However, the heroes will often investigate the villain's grievance themselves and will complement stopping the villain with taking down the offending party as well.
Either way, it's a common end result of Jumping Off the Slippery Slope. Their favorite phrase is I Did What I Had to Do—unless they are also the Tautological Templar and believe that what they do is good because a good person like them does only good things. They are not afraid to sacrifice themselves for the cause.
Often a Tragic Hero that became an Anti-Villain, and sometimes a Worthy Opponent or even Reluctant Warrior. The extreme of this is the Knight Templar who fully believes that they are in the right and the best way to save the world is to remove free will. Vigilante Man is a case where the Well-Intentioned Extremist hasn't (yet) descended to the point of not caring who gets hurt. Often ends up in rivalries with the Knight in Sour Armor. Some of those seeking to bring about a One World Order to end international strife may count as this.
Contrast with Necessarily Evil, where the villain in question has a Heel Realization and recognizes that he deserves punishment (of course, he may always choose to just Ignore That Epiphany). Often The Unfettered. See also A Lighter Shade of Grey. A staple trope of the Master Computer gone mad. If the positive intention is overthrowing an evil government, the Well Intentioned Extremists will be an example of The Revolution Will Not Be Civilized. If his extremism actually succeeds in making the world a better place, it's The Extremist Was Right.
As this trope often goes hand-in-hand with the Face Heel Turn, expect spoilers.
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