This is the character who can commit themselves to a single goal completely, absolutely, and unflinchingly. In pursuit of a goal they have no limits, inhibitions, or fear. Nothing chains them or holds them back (thus the name). You cannot make them flinch or falter. They cannot be intimidated, blackmailed, coerced, or otherwise convinced to back off from achieving their goal. There is no sacrifice they are unwilling to make or principle they are unwilling to compromise.
Fullmetal Alchemist: Shou. Effing. Tucker. He was willing to experiment on his own wife, daughter and even himself in the anime and turns them into mutated chimeras if it meant furthering his research.
By the standards of Full Metal Panic!? Fumoffu (but not the main series, where he's shown as part of a military structure), Sousuke is an example of The Unfettered in that he is utterly unbound by (and indeed incapable of understanding) the fetters, norms and standards of modern society. Instead, he operates on soldier logic. He isn't entirely there (mostly due to Kaname and her Paper Fan of Doom), but generally has absolutely no concept of 'Fair Play' and 'Proportionate Response'. The results are... Interesting to say the least.
In Saiyuki, Ukoku Sanzo aka Nii Jiyeni is the Zen philosophical version of this trope: he's come out the other side of Nietzsche Wannabe and fully embraced his own interpretation of the concept of "hold nothing", which is one of the series' main themes. He's one of the series' most frightening villains as a result.
The Major from Hellsing, his only goal is to wage war, he doesn't care who wins, loses or dies so long as the war is waged.
The Operative from Serenity.
Clyde Shelton in Law Abiding Citizen. After his family is murdered and the D.A. cuts an insanely inadequate deal with the culprit, he becomes singularly focused on the goal of not only getting justice, but bringing down the broken, flawed, and corrupt justice system that he believes failed his family.
Collateral gives us Vincent, the hired killer who's as charming as he is terrifying.
Captain Ahab from Moby Dick
William Blake's Proverbs of Hell encourage this kind of attitude:
The road of excess leads to the palace of wisdom;
The tigers of wrath are wiser than the horses of instruction;
One law for the lion and ox is oppression.
Martin of "The Dresden Files" fits. "Red Court is evil, hence Red Court must be destroyed. What does "other moral considerations" mean?"
Stannis Baratheorn from A Song of Ice and Fire. His dedication to his principles as a goal in itself approaches levels of The Unfettered, but the chapters seen from Davos' point of view also shows that Stannis himself is conflicted by this.
The Vatican's elite Iscariot Organization in the anime and manga Hellsing. Not that the protagonists are much better.
The Holy Iron Chain Knights in Berserk are devoted to smiting out all traces of evil. The problem: they include "anyone not following our exact procedures for demon-smiting" under "evil". Because of a prophecy about a Hawk of Light, which they consider the newly-reincarnated Big Bad Griffith to be, and a Hawk of Darkness, which they consider Anti-Hero Guts to be (though it's actually Griffith as Femto), things go downhill in a hurry. Doubly applies to Inquisitor Mozgus, who believes in horrifically torturing people to "expiate their sins". The thing is, the Holy Iron Chain Knights are supposed to be strictly a ceremonial guard consisting of young noblemen whose parents wanted their heirs to have all the prestige of military service with none of the danger. It is their leader, Farnese, who is completely and fanatically dedicated to the cause. She gets better, thankfully.
Tengen Toppa Gurren Lagann's main antagonists are mostly this trope.
- Some fans view the Anti-Spirals as being thoroughly evil examples of Knight Templar, due to their repeated crossings of the Moral Event Horizon. First, they turned Lordgenome to their side against his will, making him massacre his own people. Second, they turned Nia into their slave, and then tortured her, ripping her apart from the inside. Finally, the reason they tortured her? They were sick of merely oppressing Spiral races, and wanted to Kill 'Em All. Oh, and in The Movie, the torture/interrogation scene? It involved Naughty Tentacles.
The Operative in Serenity is another example - he truly believes in the ultimate rightness of his actions, even as he acknowledges that they are horrible and he is a horrible person for doing them, and as such, he will have no place in the perfect world that he is trying to create.
The Jigsaw serial killer in Saw does not consider himself a killer. Oh, sure, he acknowledges that his actions frequently lead to horrible death, but he never pulls the trigger. And he firmly believes that the people who survive his themed deathtraps will overcome their sins and become better (though this never actually works).
- He kills his apprentice because she doesn't allow for her victims to actually have a chance of escaping their traps.
Bartleby in Dogma, once he snaps. Loki seems like this at first, but really, he's just doing it cause it's fun.
The Christians in Agora. Special mention must go to Ammonius, who is this Up to Eleven and to the point of Stupid Evil. The pagans aren't much better, though, doing a Too Dumb to Live move, attempting to avenge "an insult to the gods".