Game of Thrones has Eddard Stark embody this trope and it does him far more harm than good. His demeanor is portrayed by parody in the trope's image. His eldest son Robb also inherited it from him.
Maester Aemon gives an especially poignant defense of this trope, explaining that it's easy for men to do their sworn duty when there's no personal cost. It's only when that oath is upheld in dire circumstances does it ever mean anything.
In the classic Star Trek: The Original Series episode, "Spectre of the Gun", Kirk becomes increasingly desperate to escape the surreal nightmare Death Trap he and his landing party are thrust in. However, when the sheriff suggests he ambush the Earps to murder them, Kirk becomes nearly hysterical that he cannot stoop that low regardless of how dire the situation is. However, after the party figures a way to beat the trap, Kirk keeps to that same principle to spare the defeated Earps and that act impresses the aliens to not only let Kirk's party go, but also open up relations with the Federation. Thus by keeping to his principles, Kirk pulls a real victory out of the affair instead of mere survival. The same thing happens in "Arena" when he refuses to finish off the Gorn. Although by that point the Gorn wasn't in any shape to take advantage.
Ironically, the outcome of "Spectre of the Gun" was due to Executive Meddling. In the original script, Kirk does let pragmatism trump honor, and shoots Wyatt Earp in the back. The aliens release Kirk not because they're impressed by his principles, but because, having read his mind, they know he believes in honor, and conclude that for him to have violated his own principles, he must be insane, and therefore not culpable for his actions.
Also prevalent in Star Trek: The Next Generation, especially in the episode "I, Borg". Picard decides not to take a once-in-a-lifetime opportunity to destroy the Borg, an entity that had cut through the galaxy like locusts, including assimilating Picard himself, because to use a newly individualized Borg against his race would be wrong. Somehow. Picard was severely reprimanded by his superiors for making that choice and, later, he admits that while what he did was the moral thing to do it may not have been the right thing.
The idea was that it would be wrong because the newly individualized and presumably innocent Borg would also be killed. Also, Picard hoped that its individuality would spread through the collective, so that the Borg would no longer be enemies or would at least be a group that could be negotiated with. And it worked, except only a part of the Collective was "infected" with individuality (implying that the other, more lethal option would have only taken out part of the Collective as well). Too bad Data's Evil Twin Lore manipulated them into becoming vicious conquerors.
In the episode "Half a Life," an alien is about turn sixty, an age where people on his planet commit ritual suicide as a way of preserving their dignity. When he wants to break tradition in order to continue research on how to save the planet's dying star, they inform him that, even if he finds a way to save it, they would reject it because he broke tradition.
Star Trek: Deep Space Nine gives us the Jem'Hadar. They are programmed to obey the Vorta without question, even when they know better. In one particular instance, a bunch of half-dead Jem'Hadar walk right into a Federation ambush their Vorta sent them into, knowing beforehand he was doing it on purpose so they'd all die and he could defect, simply because they are bred to obey. This serves to make them surprisingly relatable in several episodes.
Sisko: "Do you really want to give up your life for the 'order of things'?"
Remata'Klan: "It is not my life to give up, Captain – and it never was."
The Vorta are likewise bred to obey the Founders. While they never have so suicidal an opportunity to demonstrate this, their loyalty to the Founders is shown to trump reason on occasion. We also see a few surrender or defect though.
Worf is one of the most prominent examples of a character following his personal brand of honor no matter what (though sometimes it puts him in conflict with the all-forgiving sentiments of Picard's brand of honor.) But the archetypal example comes in a Deep Space Nine episode where Worf battle's and defeats Jem Hadar soldiers in order of increasing difficulty not being given time to heal between battles to the point where fellow Klignon General Martok tells him that honor has been satisfied and he still gets up and keeps fighting. Eventually the Jem Hadar chief surrenders out of respect though he could have easily won the fight and is immediately killed by his pragmatic Vorta superior for his gesture.
In Star Trek: Voyager, Captain Janeway turns down many opportunities to get the crew home by refusing to violate the Prime Directive. The irony there is that her willingness to violate the Prime Directive in the first episode is what left the ship stranded.
Janeway's first officer, Chakotay, at times exhibited this attitude as well; usually in confrontation with Janeway during one of the many instances where she was entirely willing to break the rules. Chakotay is probably one of the most consistent (if not well-known) examples of this trope, after Game of Thrones Ned Stark. This was frequently at odds with his original status as a major leader in a guerrilla army/ terrorist group and the way he ran it, though considering that he became a Maquis due to considering it to be the morally right thing to do, he may have been this even as a terrorist.
Chakotay was a Starfleet officer before his defection, so he may still believe in he ideals of the Federation.
In Firefly, Captain Malcolm Reynolds chooses to take in and shelter Simon and River Tam, despite the fact that having them on board increases the danger to his crew and actually puts all them in danger multiple times. When asked why he would do something so risky for people he barely knows when he seems like such a rational, cold-hearted bastard, he doesn't respond, tries to avoid answering altogether, or offers some flimsy excuse that everyone can see through quite clearly.
Though this trope applies once they've become part of his crew, his reason for offering that protection in the first place probably come down to a simple Take That against the Alliance.
The Big Damn Movie shows this in one of its more powerful scenes: After River's psychotic rampage, and when Mal is confronted with every rational reason to leave them behind, he still chooses to protect them and fight for them.
Mal is still brutally pragmatic, though, especially when dealing with threats to his crew. Case in point: him kicking Crow into the ship's engine after he declared they would meet again in "The Train Job," or when he decided to shoot the Operative as soon as he said he was unarmed in Serenity. That's what we like about Mal: he has honor, but not stupid honor."
Or most times he does. On occasion, though, fighting for honor means Mal risking very likely death, which Inara once calls him on and points out how senseless it is. And, of course, much of his fighting against the Alliance (equally risky) probably IS an honor thing for him, including the less honorable criminal stuff (which is the only way he can justify it, and sometimes not even then).
Mal does make it a point to help out people who are in dire straits, though; in "The Train Job," the moment he finds out the cargo he stole is medicine for the dying villagers he chooses to return it. When the local lawman remarks that people have a choice to make when they find out the details of a situation like theirs, Mal's only response is that he feels they don't have a choice at all.
Even Jayne has a few instances of this. One particular example is in "War Stories," where he outright tells the rest of the crew that going to rescue Mal from Niska's army of thugs is insane and a suicide mission. Later on, as everyone is preparing to go on the rescue mission, Jayne appears, fully loaded with all of his guns and ready to do his part. At the surprised look of the rest of the crew, his only response is a confused "What?"
It's also worth noting that Jayne could have easily left both of them there to distract the Feds and make a clean getaway, but he still helps them escape.
Maybe he just didn't think of it.
Simon also does this for River, and he strictly follows the Hippocratic Oath even when he might risk capture or when it's someone he doesn't particularly like.
One episode of Lawand Order features a serial killer's public defender who, acting on a tip from his client, goes to see a warehouse where the killer has stored bodies of his victims, which he admits was stupid but refuses to tell anyone where they are, standing firmly behind privilege. Because he had to lock it when he left, thus helping hide the bodies, McCoy decides to charge him as an accessory, while making it clear that all the lawyer has to do to get the charges dropped is give up the location of the bodies. He never does, and goes to prison still refusing.
Buffy the Vampire Slayer tends to follow this trope when it comes to Buffy dealing with a human threat, at least until the Bringers (were they human?). She lets a werewolf hunter leave even though judging by the collection of teeth he's killed dozens of people to get werewolf pelts. She refuses to kill her friend Ford, who betrayed her, until after he becomes a vampire.
Perhaps the most extreme case is the fifth season, when she has to choose between saving her sister or saving the universe. She threatens everyone with death if they go near her sister. Then she takes a third option. It is such an extreme case that one could say she acted as a Principles Zealot, although either way it also fits this trope as it is very unreasonable but according to the strict deontological ethics of a Principles Zealot, one can never kill an innocent human, even to save the whole world. Giles' consequential view, that Dawn should be killed if there is no other option, seems much more reasonable even if one isn't usually strongly consequentialist, but the point of the trope is that reason is being discarded.
The Doctor could easily, easily wipe out the alien threat of the week, but he insists on giving them a choice, usually involving finding another world for them to settle on, free of intelligent life. It's only when they refuse that he shows them why that might have been a good idea.
A perfect alternative example appears in the 1996 TV movie; a police officer is preventing the Doctor and his companion from reaching their destination. Time is running out, the entire planet Earth is at stake, and the Doctor doesn't have time to reason with the police officer. So he swipes the officer's gun. However, he is also not the kind of man who points guns at innocent people, no matter what the situation. So he points the gun at himself and yells "Now stand aside before I shoot myself!"
The Eighth Doctor hasn't changed in this respect by "The Night of the Doctor", either. He attempts to save a young woman from a crashing spaceship, but she refuses to go with him so he refuses to save himself.
Gets more than a little Anvilicious when the Doctor opposes eliminating the Daleks, even though they're dedicated to wiping out all non-Dalek life in the universe.
The Doctor's attitude makes more sense when you consider that he's terrified of losing his morals and becoming something like the Valeyard. If he agreed with genocide or murder, even once, even justifiably, he'd be taking a first step down a disastrous road, and he wants to avoid that at all costs. Remember the Time Lord Victorious? That was but a glimpse of what he could become.
Additionally, the Time War could have been so awful that the idea of annihilating the Daleks brings up horrible memories.
In the classic series, the Doctor had the opportunity to wipe the Daleks out at the moment of their creation, but wasn't sure he had the right, and concluded that humans and other races opposing the Daleks was what led to galactic harmony.
One of his worst moments was in the new series, when he met the Sontarans, a race of cloned soldiers, whose one notable weakness is a vent in the back of their necks. It's in the back because Sontarans are not supposed to retreat, so it's a relatively safe place to put it. He has a bomb that can destroy the Sontaran ship and save the Earth. But he decides to beam up to the Sontaran ship WITH THE BOMB in order to give them a chance to surrender. Never mind that anyone with even the smallest knowledge about the Sontaran would know that the Sontarans don't surrender, the idea that the ship in question wouldn't gladly be destroyed to be able to defeat someone as famous and powerful as The Doctor (Not to mention, stop his occasional ruinings of their war effort) is absurd. In the end, another character had to sacrifice himself to save him. Way to go, Doctor.
This also comes up pretty much any time the "Rules of Time" get invoked. So the one Dalek who escaped the Time War, over thousands of years, becomes a half million Daleks, causing untold misery on Earth in the meantime. So does the Doctor just take the time machine at his disposal, go back in time, and fight the Dalek when there's only one of them? Of course not. When the Doctor tries to bring Rose back to her home, but accidentally arrives one year too late, causing Rose to have been listed as a missing person, her boyfriend to have been arrested for supposedly murdering her, and lots of trauma suffered by her family members, you'd think this would be easily fixable by just getting back in the TARDIS and getting it right this time, but that never even comes up. Even yanking Adric off of the crashing ship he's on is quickly shot down thanks to the Rules of Time, even though doing so wouldn't have altered history at all, as the ship still would have crashed, and the resulting aftermath would have been the same.
Subverted by the eleventh Doctor. He tries to talk if the situation allows it and tries to spare manipulated pawns, but against actively hostile forces he will wipe them out as soon as he has the advantage.
Helo on Battlestar Galactica, the fact that his wife Sharon is a Cylon makes his journey much tougher.
In The Sarah Connor Chronicles, which tosses out the events of Terminator 3, both John and Sarah try to stop Skynet with no deaths. Cameron and Derek Reese don't share the same sentiment, however. If killing someone will complete the mission and possibly stop Skynet, they'll kill them in a heartbeat. This goes out the window at the start of the second season, when John is forced to witness a man attempting to rape his mother. Thou Shalt Not Kill comes to a crashing end when he breaks free. On the other hand, John refuses to destroy Cameron even after she goes berserk and tries to kill him. Everyone, even Cameron herself thinks that John should have destroyed her, but he refuses to, because he still trusts her.
Subverted in The A-Team. Even though the team usually fits the trope to a T, in one episode Hannibal secures the help of General Fullbright by promising to turn himself in if he assists him. Afterwards, Hannibal escapes and says "In war there are no promises; only strategy."
Subversion in Rome where Anthony, who is besieged in his palace with the (very) pitiful remains of his guard, counts on this trope and challenges Octavian, his sworn enemy and leader of the Roman forces, to a one-on-one duel, knowing that he is easily the superior warrior and brags that he alone is going to win the war. Octavian's answer is looking at his general-staff and asking: "Is he completely nuts???" Anthony rather stupidly assumed in his drug-addled state that Octavian would give up a supreme tactical advantage just to avoid looking like a coward, when even if Octavian cared about that he could just kill anyone who heard about it.
Rome also has a very interesting take on this trope with Lucius Vorenus. He is driven by his morals 100% and can think of nothing worse than dishonor. He stays loyal to Antony even after his death, prompting Octavian to comment: "The man turns loyalty into a vice". What makes Vorenus an interesting example is that he is so completely driven by his sense of honor and moral, but those don't exactly measure up with the ones we have today. He is, for example, prepared to kill the boy Lucius (his dead wife's bastard son) because "honor demands it". Except he doesn't kill him after all, subverting this trope for perhaps the only time in all of his onscreen appearances, which made for a Crowning Moment of Heartwarming - or at least what passes for one in this show.
Michael Weston from Burn Notice will stop at nothing to solve the problems of every and any passerby he meets. Even if he should be trying to figure out who burned him. Or if his apartment as just been blown up in an attempt to murder him.
Duncan MacLeod in Highlander: The Series is another prototype example for this trope. He would accept any challenge, no matter what the the odds, only to prove his honor. He even explained it to Methos in an episode:
Duncan: Did you know Mencius? Methos: Student of Confucius, yeah. Duncan: "I dislike death, but there are things that I dislike more than death—" Methos: "—therefore there are occasions when I will not avoid danger." Death before dishonor.
Actually justified considering Duncan is a 16th-century Highland Clansman when such ideals were very much the rule.
And utterly averted in Methos himself, who only really follows this trope when it comes to his friends. This is illustrated in the episode "Chivalry", right after Duncan MacLeod has disarmed, then released, the episode's female bad guy, Kristin. As MacLeod starts walking away from Kristin, Methos steps forward.
Kristin: "Who are you?" Methos: "A man born long before the age of chivalry." (waves his swordpoint toward her sword, which is on the ground next to her) "Pick it up."
Prince Arthur in BBC's Merlin has demonstrated this trope repeatedly, as far back as his risking his life to save Merlin in 1X04, all the way up to literally putting his neck on the line to keep his word to Morguse in late season 2.
Also Lancelot. Much to Guinevere's exasperation, it's almost as if he and Arthur are in some kind of competition as to who can be the most stoically self-sacrificing. (Lancelot's winning).
A good concrete example with Percival in the season 4 premiere. Percival stumbles across three frightened children, realizes he can't carry all of them and a torch (the only defense against the Dorocha), so he drops the torch and carries the children. Predictably, the Dorocha close in on him, but Elyan pulls a Big Damn Heroes moment to save them all.
In Season 2, Tara chose to put her alliance with Chris & Alex over the Race, and even over her own teammate, and it eventually cost them the Race.
Erwin & Godwin (a.k.a. the Cho Bros, from Season 10) formed the infamous Six-Pack alliance with David & Mary and Lyn & Karlyn (two teams most perceived as fodder). They then proceeded to sit around at tasks, after they were already done, waiting for the other teams in their alliance. Even their own alliance members thought this was stupid.
The formerly engaged team of Dennis & Erika (Season 5) became the first team out when Dennis, who wanted to prove that he wasn't a "scumbag" after another team called him that earlier in the leg, let all the other teams get cabs before him and Erika. He did get a Consolation Prize, however (other than the trip given to them by Colin & Christie after the race), in that this act appeared to re-spark his relationship with Erika.
In one episode of Blue Bloods, Jamie (the Reagan family's Knight in Shining Armor) is asked by the FBI to help them investigate possible corruption in the NYPD. Jamie refuses and decides to carry on his own investigation alone—because it could potentially involve his family and it is more honorable for him to look at it first before deciding. In doing this Jamie is putting himself in considerable danger without backup. But that's Jamie.
Noah's Arc: This is one of Noah's more frequently seen characteristics, such as in one episode where he turns down a $4000 check from Wade because he feels he should get himself out of his financial mess (despite having to sell his beloved car to do so).
A spoof on this occurs at the beginning of Due South in which Fraser pursues a perp through miles and miles of frozen wasteland. Finally he brings him in, plops him at the Mounties' office and says, "That's the last time he'll fish over the limit."
Delen always at least seems like the sort of person who would put Honor Before Reason. In fact she several times does what she has to do and once or twice what she definitely doesn't have to do. But she always gives the impression of putting Honor Before Reason, prefers that as her default, and sometimes has a Crowning Moment Of Awesome while doing so. When told that Neroon is coming to assassinate her, Delenn forbids Lennier to tell Sheridan, believing that the Minbari people should deal with their own internal dirty laundry without foreign interference.
Minbari generally think they are putting Honor Before Reason. The real picture is more complex and depends on which Minbari you talk to.
When Londo orders Narn evacuated because he gave his word to G'kar, he says "All I have left is my honor."
The Expanded Universe adds the Rogolon, a Proud Warrior Race fixated with one-on-one duels. This bit them back in the ass hard during the Centauri-Orieni War: when the Centauri invaded them to bypass the Orieni lines, the Rogolon ships advanced one at a time issuing their challenges to the invaders, resulting in the Centauri (the local poster children for Combat Pragmatists and Obligatory War Crime Scene) to gang up on their ships until there was nobody else to oppose their passage.
Doug Ross on ER was driven to do what was right for children, regardless of the consequences to himself or his career. That's admirable, but he was also very short-sighted when it came to the consequences of his actions to his friends and colleagues, and eventually left the hospital in disgrace due to some very questionable decisions.
Bates of Downton Abbey is very much this, refusing to tell the Earl of Grantham that Thomas was the real thief when he's framed for theft (twice!) despite Thomas's constant bullying of both him and everyone else, because he doesn't want to be the cause of Thomas losing his job.
Matthew Crawley is even worse. First, he insists that he will still marry Lavinia even though she has seen him kissing Mary and has realised that he doesn't really love her. Later, he stands to inherit a great deal of money from Lavinia's father, which is great news for the family as Lord Grantham badly needs a fortune to hang onto his estate - but Matthew is unwilling to accept it as he is certain that Mr Swire must have left it to him thinking that Matthew really loved Lavinia.
Once Upon a Time: The Evil Queen has called Snow White to a parlay, meaning that Snow cannot bring weapons. Snow agrees, and insists that she has to abide by the rules. Grumpy and Red both in no uncertain terms tell her that this is a bad idea, and Red even says that Snow is "too noble for [her] own good." (What isn't mentioned but is important is the fact that Snow isn't allowed to bring weapons, but the Queen has magic, so she's bringing a weapon just by showing up.) This is how she ends up eating the poisoned apple that puts her to sleep.
Later, When Snow finally subverts this and preemptively kills Cora by turning her own magic against her before she and Regina could become the Dark ones and murder her entire family, she spends the next episode moping about and even begs Regina to kill her, and then it is revealed that the powers that be for that universe branded her with a black spot on her heart for the act.
Person of Interest: A former soldier and Afghan War veteran robs banks because he believes he has a debt of honor to repay and needs to support the family of a friend who died in Afghanistan after they switched seats during a mission.
When Captain Gregson in Elementary realises his ex-partner framed a serial killer, he says that if the guy turns out to be innocent, he'll have no option but to report her. When she asks if he realises what that will do to his career, he says it'll end it, but that's not the point.
Koragg in Power Rangers Mystic Force is this trope. About midway through the season, the bad guys manage to strip the Rangers' powers and win. Koragg helps the Rangers get their powers back, because he didn't like the way the victory was achieved. Nick even lampshades this.
"You want darkness to take over the world, but only if it does it nicely?"
In Bangkok Hilton, Hal asks Richard to take his daughter's case, in spite of his inexperience with criminal law and the damage it could do to his firm if a white lawyer defends a white client on a drug trafficking charge.
Richard: I can't help but ask myself, Hal, where's the profit in this?
Hal: She's innocent. To some men, proving that would be profit enough.
Richard: Oh, to some men but not me, is that it? Well, that's where you're wrong, Hal, because I'll tell you what else I've been thinking. Above all, I'm a lawyer, and if I don't use the law now to defend an innocent person, then, it doesn't mean anything, does it? So I think we'd better do it. We'd better defend her and damn the consequences.
Shows up in the Arthurian episde of MythQuest, naturally. Particularly, after things go horribly wrong, Alex opts to accept the beheading he promised to Eliavres a year earlier instead of touch the window and get back to the real world.
JAG: In "The Colonel's Wife", the eponymous wife has involuntarily become a drug courier in order to protect her husband's anti-drug program in Panama from blackmail. When the facts are about to be revealed, she gets herself killed in order to save her husband's honor.
Breaking Bad may be one of the only times this is portrayed negatively. Walter White, the Anti-Hero, declines money from his very wealthy former friend to pay for his cancer treatment, opting instead to cook meth. He does this out of Pride as the money comes from the company that he co-founded but dropped out of at the wrong time. Rather than showing his inner good, it shows that from the beginning that he was a selfish and petty man who lets his Pride rule everything he does, deciding to turn down money that could help his family in the long-run because of it. It also serves to foreshadowthe kind of man he eventually becomes.
In Princess Returning Pearl, pretty much all "good" characters emobdy this trope, however there is one scene where it shows itself most clearly. Xiao Yan Zi, Yong Qi, Er Kang and Zi Wei have just commited a major crime and the emperor Qian Long is throwing them in jail. The Empress Dowager and Ling Fei manages to pretty much convince Qian Long to let Yong Qi go free because he is the emperor's son. The idea that if he isn't imprisoned, he could help rescue his friends. But apparently holding the Idiot Ball, Yong Qi declares that he would rather go to jail with his friends than go free without them. You can see both Ling Fei and Er Kang mentally facepalming.
Several of the Friends cast display some shades of this trope. Monica would rather do everything she can to get people to like her and have her be the best hostess (or whatever she wants people to come over for) instead of accepting the fact that she doesn't have to be the best at everything. Joey refuses to accept Chandler's offer of loaning him money due to his pride. Ross refuses to admit he is wrong when he is actually wrong, which is one of the huge plot drives for the infamous break up between him and Rachel.