The Exalted Torture is usually someone who considers using the Jack Bauer Interrogation Technique, Perp Sweating to the degree of outright Police Brutality, war crimes and similar atrocities, and/or other actions like most people consider using periods. But he's not portrayed as evil or in a negative way.
He's the Hero.
In a nutshell, the Exalted Torturer is:
Viewed as heroic and admirable when his actions are things villains in other (or even the same) media would do. Which at extremes can be extreme Designated Hero territory in line with acting For the Evulz, where the character will do things that would make "villains" or "antagonists" flinch.
Try and be fairly good people. They at least try to have decent morals, try to do the right thing, and acknowledge on some level that some of what they do is unpleasant but are doing it only for the sake of a good higher purpose.
They generally exist as good guys of The Federation or The Kingdom in fiction where the "Black" in the local Black-and-White or Black and Grey morality is Very Black even in comparison to any greys, and you can see the Godzilla Threshold just looking over your shoulder. Though in some cases they can show signs of enjoying it toooo much, they usually don't let it override their moral compass.
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.
The protagonist of the Hanzo the Razor films. 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.
Prisoners has a father resort to this, over the whole film, by torturing the main suspect to reveal where his missing daughter is being held.
Dan from Zero Dark Thirty was one for the first part of the movie, though he eventually had enough and left to work at Langley.
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.
Jarod from The Pretender does some pretty dark things to the people who hurt the blameless victim of the week. These often involve making them believe they will die painfully.
Wonder Woman of the Wonder Woman 2011 Pilot is one of the few women who could qualify. And she doesn't have entire cities at risk, she just deals with drug dealers who sell drugs with dangerous side effects.
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.
Andrei Koscuisko of the Jurisdiction series by Susan R. Matthews is both a Torture Technician and an Exalted Torturer. His job is necessary and he's good at it. And, much to his unending horror, he enjoys it.
Terry Thorncove of the novel Inner Dark by Zhenmei Li is a complicated case. He started out as a Torture Technician, became The Atoner, found the side he switched to was willing to use him for 'special' interrogations, is viewed by the higher ups as a great hero but by his friends as the Token Evil Teammate, is portrayed as a noble man resisting a dark urge in the narrative, continually invokes Drowning My Sorrows over his actions and by the end is more or less dead inside.
Mythology and Religion
Often, Satan is described this way, getting his jollies off by tormenting people (and lesser demons) in Hell. Sometimes, he is even described as playing a pivotal role in the actual judgment process, as more of a Villain Protagonist. In fact, the name derives from an old Hebrew word, ha-satan, which translates as "The Prosecutor."
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.]