Lawful Stupid

Obligatum VII, the definition of Lawful Stupid.

Lawful Stupid is gamer slang (it is derived from the Dungeons & Dragons alignment system, but can easily be applied to characters in any role-playing game -- in fact, it can be applied to characters in any medium, or even real life) for a specific way of playing a Lawful Good or, especially, a Lawful Neutral character, usually a Paladin. It is characterized by lack of common sense, following the rules arbitrarily without actually understanding them and just generally being an annoying prick. He's that guy who will stop a chase scene because he has to chastise someone that was jaywalking. Lawful Stupid players are one of the main reasons (along with asshole DMs) why people dislike the Paladin class.

It can also be a jab at the fact that Intelligence is a common dump stat for Paladins, since thanks to their MAD they require high Charisma and Wisdom (the traditional dump stats of combat classes).

Although the iconic Lawful Stupid character is a poorly-played Paladin (Alignment requirement: Lawful Good), non-Paladin depictions are almost invariably Lawful Neutral, since this kind of characterization is a disappointingly logical extrapolation from a character alignment that can be summed up as "the Law is the Law and all that matters is that it is the law; whether or not it helps or hurts people is irrelevant, the LAW must be upheld!"

Compares to Chaotic Stupid, Stupid Evil, Stupid Good, and Stupid Neutral. There really are a lot of ways to be stupid in fantasy games, aren't there?

Examples of Lawful Stupid

• The Inevitable, which are divine golem-like beings with the duty to uphold laws and correct the broken ones. There's a story of one named "Obligatum VII" (the seventh in its line because six time prior people had the common sense to stop him) who trying to free the BBEG in a campaign. The story goes that some mages summoned an eldritch abomination named Pandorym to get a fair bargain with the gods. The wizards imprisoned Pandorym instead of finishing the ritual to let it loose so that it wouldn't destroy the universe before they were ready, but the gods just smote the stupid wizards the instant they were done imprisoning Pandorym so he's stuck. Well, Obligatum is here to set things right, and make sure that poor, imprisoned omnicidal maniac gets the freedom it was promised to carry out its goal, which through some warped sense of honor it is willing to do. An omnicidal maniac who is powerful enough to destroy the entire universe regardless of whatever feeble resistance the universe's inhabitants can muster if Pandorym's mind and body were ever to be reunited. How exactly this does not bring him into conflict with another type of Inevitable, the Varakhut, whose job it is to prevent deicide is a whole other box of worms.
• The Harmonium from Planescape. The Harmonium believes that peace is a better end than war. [...] If it takes thumping heads to spread the truth, well, the Harmonium's ready to thump heads. Sure, there may not be peace right away, but every time the Harmonium gets rid of an enemy, the multiverse is that much closer to the universal harmony it was meant to have. This attitude is how the third layer of Arcadia shifted into Mechanus, and the gods of Arcadia had to start over. Whoops.
• The Modron race, similarly to the Inevitables above, due to being extraplanar mechanical lifeforms who embody the Lawful Neutral environment. Except they have even less personality. Imagine a cheap 80s computer with arms, legs and the ability to beat you over the head; that's basically a Modron. They can't even understand the idea that their assumptions may be incorrect.
• The stereotypical Space Marine. Stealth is cowardice, frontal assaults are the only way to go. On the occasion they do utilize tactics like stealth, feints, and flanking, it's all to help the frontal assault succeed rather than the other way around. Retreating is never an option, even if it's to gain more cover. Some will never field psykers, ignore xenos, and some won't even cooperate with other Space Marine Chapters. A special case being Leandros.
• The Starks from Game of Thrones. When Ned Stark finds out that Joffrey and his siblings are incest born bastards, he does the most asinine thing possible and tells Cersei, instead of going to Robert directly. He also tells his daughters of his plan, which causes Sansa to blab to everybody. His son Robb Stark has even more fuck ups, namely executing one of his top generals when he should have kept him around, failing to communicate with Edmure (though Edmure is incompetent), and blatantly breaking his promise to Walder Frey because he felt bad he screwed some other chick and decided to marry her in order to keep their honor intact. Admittedly, he is still a kid in the novel.
• Rorschach from the Watchmen comicbook is this considering his utter devotion to principles. It's best illustrated in his quote "No. Not even in the face of Armageddon. Never compromise." It's later shown that he does not mean that metaphorically. He's an interesting example because he is perhaps the least 'good' of the main characters (with the exception of Comedian maybe) who has no problem with killing even when it's probably not necessary, and with absolutely no empathy. But at the same time he has his code and he sticks to it, even when it is directly stupid of him to do so. Not compromising is an absolute hallmark of lawful stupid.
• The Jedi from the Star Wars Prequels are this, as they followed the Jedi Code - which was meant as a mere guideline - as a set of unbreakable rules and set out to completely repress all emotion in somewhat unfounded fear of those emotions leading to the dark side, when they should have acknowledged that which makes us human and simply taught how to use them positively. Such arbitrarily following of the code leads the Council to turn a blind eye to the various problems Anakin Skywalker was having, thereby unintentionally sealing their own downfall.
• The Dwarfs from Warhammer Fantasy. They are obsessed with the concept of revenge which causes them to wage many unnecessary wars, which is especially stupid since they are a dying race. This behavior is even enforced by their gods. When two dwarven lords were fighting each other in a fortress that was currently under assault by orks they eventually realized that neither of them remembered what they were fighting over and decided to put aside their differences to actually defend against the orks beating down on their gates. Both sides were promptly crushed by the gods themselves.
• Javert from Les Miserable. Properbly one of the oldest contestants on this list, Javert is the police-inspector who relentlessly pursues Jean Valjean throughout 17 years, after Jean chooses to ditch life as a marked man and begin anew. Sounds extreme? Well, Javert was in charge of Jean when he was working his ass off in prison too. Jean got there by stealing a lump of bread to feed some children. He got 20 years, 5 for the bread and the resisting arrest. So when Jean chooses to not live the rest of his life with a paper on his person saying that he was a former convict, Javert's internal Justice Alarm went all haywire. Javert himself was brought up in prison, where there are only two allignments: the Law or the Convicted. Javert chose Law, and since then no one should escape their by-God-decided punishment. In fact, when Jean spares Javert's life when he could have ended the merry game of catch-the-convict-who-got-his-life-back by killing him, Javert meets a moral wall - His world is so extremely black and white, that the idea of a criminal doing good deeds is completely impossible to him. He knew that taking Jean now would be to punish a true child of God, and so did the only thing that made sense - to execute himself for insubordination. Would have made a damn good Commissar, that one.
• Most modern robots. If a robot makes a mistake, it won't correct it despite it being wrong it will just do what it's told, over and over and over again regardless of the results.
• Saradomin from Runescape, while well meaning for his followers. He started a god war in Naragarun world plane that led to it being attacked by way more destructive gods and as a result have a lot of people looking poorly on him for that kind of shit.

How to avoid it while playing lawful good

Required Reading: Discworld by Terry Pratchett, in particular anything having to do with the Witches of Lancre or the Ankh Morpork City Watch, especially Sam Vimes and Carrot Ironfoundersson. Carrot might not be very savvy when it comes to subtlety, but he is very much a good man, if a bit odd and literal at times. Some folks would argue that Vimes is Chaotic Good rather than Lawful Good, but fighting over alignments is for the alignment page -- the point is that he and Carrot are decidedly not Lawful Stupid.

Another way to play lawful good is to play your paladin like a modern soldier: able and willing to do anything needed to win, but still bound by the laws and customs of war, for example the Geneva and Hague Conventions. Those laws still restrict the actions of a soldier but he is still expected to act with common sense in order to achieve victory and not follow orders that violate those laws.

How to avoid it while playing lawful neutral

This is arguably even harder than avoiding it whilst playing Lawful Good; at least Lawful Good types are supposed to balance their calling to law & order vs. their calling to good. Lawful Neutral types are categorized by their firm belief that law and order are the only things of importance, with morality being dismissed as insignificant next to maintaining of order. The primary key to doing so is to keep a proper perspective; traffic laws, for example, have their place in the scheme of things. When you are racing to prevent the nuclear annihilation of a city is not that place. Don't get so bogged down with legal minutia that you allow far greater acts of destruction and anarchy to occur in whilst you attend to the little things.

Judge Dredd can be a good example of this. For example, in the opening sequence of the 2012 Dredd movie, he pursues a car full of criminals but does not shoot at them until they collide with and kill a pedestrian, and even then only shoots to disable the van's tires. He doesn't shoot to kill until one of them threatens to kill a hostage and refuses to accept an offer to surrender. Also, when he sees a vagrant sitting outside the crime scene Dredd tells him not to be there when he gets back instead of arresting him because he has better things to do at the moment. Of course, when he's just doing the rounds on his birthday, he'll issue noise citations to children who sing to him because he is The Law (and then donate the presents he receives to an orphanage because he's not That Guy).