Viewed as heroic and admirable (not an Anti-Hero or Villain Protagonist) when his actions are more in line with acting For the Evulz, doing things that would make "villains" or "antagonists" flinch at the idea.
Rapeman. While the manga and anime are arguably satire featuring Black Comedy Rape, that doesn't stop some people from blaming the rape victims for their rapes, believing rape is an okay punishment, and somehow seeing Rapeman as a righteous hero rather than Crossing the Line TwiceBlack Humor in an Evil Versus Evil world.
Ibiki Morino from Naruto, who is actually one of the good guys. Despite his reputation though, his methods are largely psychological.
Saito Hajime of Rurouni Kenshin believes strongly in justice, but it's hard to deny that he really likes killing people. While he doesn't torture on-screen, at one point, he dissuades a boy from taking revenge on his parents' murderer by telling the boy that the murderer will undoubtedly have information tortured out of him before being gruesomely executed, and thus letting him be arrested would be the better revenge.
Comic Books
Sin City's Marv not only does this to criminals but he loves it. There is an entire monologue in his first story about how much he enjoys what he's doing.
The protagonist of the Hanzo The Razor films, who was once this page's picture before the cleanup. The same as the Rapeman example, except not played as satire and Black Comedy. Instead, he's played straight as a "good cop" who investigates his cases by raping his suspects into submission.
The Dark Knight Saga sets the following baseline for Batman: If you are a Smug Snake of a dirty cop, he won't hesitate to traumatize you and scare you half to death as a form of interrogation. If you're a crime lord holding out information on a madman going on a destructive rampage through his city, he will go even farther. If you are said madman and the clock is ticking on people's lives, he will start at bodily harm and beat you within an inch of your life if that's what it takes. The Joker sees all this and, with mixed awe and annoyance, declares him "incorruptible" (because he has only one rule, "no killing", and he won't break it).
An in-movie example in the 1939 The Hunchback of Notre Dame: the official flogger who publicly whips Quasimodo is cheered like a sports hero.
Wesley Wyndham-Pryce from Angel probably falls into this trope when he tortures Justine in early season 4. He also does this later in the season to get information about Angelus.
Sayid from LOST. He, like a number of other characters, spends time on both the Black and White sides of morality and pretty much everywhere inbetween, but he spends most of his time on the lighter side of grey.
Jarrod from The Pretender does some pretty dark things to the people who hurt the blameless victim of the week.
The M.O. of all members of the Strike Team on The Shield.
Literature
In the Ksin saga, the royal torturer is that. He is a true master in causing pain and does his worst than he works — but he also exemplifies Honor Before Reason. Even though he knows that some things he does are unreasonable, he considers it a must at his position — a torturer must be a paragon of honor or else he will be worse than a beast.
Subverted in Gene Wolfe's Book Of The New Sun. Severian at first believes this, but then comes to later realize that tortureisbad. As Autarch, Severian tries to outlaw the Torturers' Guild, saying "It is intolerable that good men should spend their lives dispensing pain." The Grandmaster responds that "It MUST be done by good men," implying that, like the Ksin example above, that torture can either be done by good men or by those who would take pleasure in it.
Depending on who you ask, God or Satan (or both) in The Bible. The book of Job is an example, where an innocent victim is tortured solely to prove his faithfulness.
In the Left Behind series, it's God who's propped up as the Exalted Torturer. Not that God or Jesus Christ enjoy it, as Jesus sadly watches the Antichrist, the False Prophet, and all those who rejected Him throughout the ages go to their appointed doom. To quote Jesus speaking to Ashtaroth, Baal, and Cankerworm in the Dramatic Audio:
"Like My Father, with whom I am One, I have no pleasure in the death of the wicked, but justice must be served, and death is your sentence."
While no details are given as to what exactly Butcher Brakespeare of the Flora Segunda books did during the war, her reputation as her country's greatest war criminal makes it clear that it was not very nice. But apparently she thought very hard about it and while it was difficult for her to do, it was the only way. So that's all right then. (Meanwhile, the other side's equally-vague war crimes are treated as completely unjustified and horrible.)
In the Lensman universe, Worsel of Velantia and Nadreck of Palain VII both unleash the torture instruments of the Delgonian Overlords upon their former masters in the search for vital information. In Worsel's case, the other Lensmen let him do it because his own species was for countless centuries subject to the Overlords' depredations (basically a combination of Mind Rape, torture and a kind of telepathic sadism, and concluding with snuff and the consumption of the dying victim's life energies), while Nadreck is a member of a species which literally cannot comprehend such concepts as suffering without years of study, and even then can't feel it.
Pulp detective character Mike Hammer did a fair amount of beating and killing perps. Notably, while this was depicted as praiseworthy in the novels, one of the notable films based on the series, Kiss Me Deadly is something of a Stealth Parody making him a Villain Protagonist.
Tabletop Games
The Gray Guard Prestige Class/Paragon Path from Dungeons & Dragons was supposed to allow paladins the ability to go all Dirty Harry on potential perpetrators without losing their alignment.
Played with in KGB founder Dzerzhinsky as depicted in Robert Bolt's State of Revolution. When he objects to a career as the ideological garbageman, Lenin asks "Should it be done by someone with an appetite for garbage?" Later when he is grilling Lunacharsky, he retorts "It was you more than anyone else who persuaded me to take the position."
Dragon Age II: During the quest "Inside Job", Hawke can torture a miner and have him killed. In his/her own home.
World of Warcraft is a special case. While most of the torturers in game (Torturer Lecraft and such) are NOT this trope because they are antagonists to both factions, there are characters that do meet this trope because at least one faction considers them non-antagonist (Sergeant Kanren in Falconwing Square is a Horde example, Interrogator Khan in Telaar an Alliance one), and there's a class (Death Knight, at least in the beginning) and quests for both Horde and Alliance that can make yourcharacterbecome an Exalted Torturer.
Web Comics
Sonichu and Christian Weston Chandler's self-insertions.
