There's a pizza commercial for one of those "already prepared ready-to-go" pizzas where a guy walks in and asks for a pepperoni pizza and the girl behind the counter turns around, grabs one, and hands it to him. He says something like "No ordering? No waiting? There's no rules!" and begins taking his clothes off. A voice in the background yells "Put your shirt back on!", which he does, still yelling excitedly, ''There's one rule!"
Averted in Psycho-Pass: in Episode 19, Professor Saiga asks Kougami what the definition of anarchy is, and Kougami replies that it is a denial of governing and authority but is intrinsically different from confusion and disorder. He then reaches the logical conclusion that this means that Makishimacannot, by definition, be an anarchist because even though his desire to overthrow the Sibyl System is genuine, he is bent on causing violence and death wherever he goes and revels in it.
As pointed out in the page quote, V for Vendetta is actually a subversion, pointing out that "mindless chaos" and "anarchy as a social system" are not, in fact, the same thing. Unfortunately, the peoples' reactions at the end of the comic (and those of many readers as well) demonstrate that not everyone realizes this.
Averted with the DC Comics character Anarky, who in one storyline is horrified to the point he gives up his plan when he is presented with reasonable evidence that anarchy will lead to chaos and will ultimately resurrect the very governments he is trying to oppose.
In The Dark Knight, the Joker clearly links chaos and anarchy together in his speech to Harvey Dent/Two-Face when he tells him, "Introduce a little anarchy, upset the established order, and everything becomes chaos."
The primary antagonist Bane, in The Dark Knight Rises. A subversion, actually. Anarchy's a tool to bring Gotham down, not something he himself believes in. Excepting perhaps the Kangaroo Court, he's clearly in charge of the city.
Intentionally averted in Monty Python and the Holy Grail, where King Arthur comes across an anarcho-syndicalist commune of literal mud farmers. They are decidedly non-violent, particularly when compared to Arthur himself, but also extremely irritating, screaming "oppression" when Arthur grabs one of them in annoyance, yelling at him to shut up.
Escape Velocity, in which the villain, a renegade Sociopathic Soldier, screams "Anarchy!" at the top of his lungs before killing people.
Averted in S. Andrew Swann's Hostile Takeover trilogy, set on Bakunin, a world of anarcho-socialists (although the hero is more of an anarcho-capitalist) under threat by the imperialistic Confederation.
Zigzagged in No God, No Master, centering around the investigation of the 1919 Anarchist Bombings, which (as the name implies) were the work of Luigi Galleani and his anarchist followers. On the other hand, it makes very clear that other anarchists did not advocate these actions. In the end, it did nothing but get many thousands of anarchists (violent or not) deported.
The Man Who Was Thursday: The anarchist organization in the book takes this position. It's pointed out that there's a difference between the revolutionary who throws a bomb to kill a king, and the "anarchist" who throws a bomb to kill anybody. However, all of them turned out not to be anarchists in the end.
As far back as the Book of Judges in The Bible, we have this quote: "There was no king in Israel those days. Everyone did as he pleased."
The Larry Niven story Cloak of Anarchy posits "anarchy parks" with just one rule: no violence (making them the anarcho-pacifist sort of anarchy). Any time a fight starts (or looks like it might start), floating robots stun all participants, who are then separated. They wake up a few hours later, and it's mentioned that the threat of losing part of your holiday is enough to keep most people in line. Then someone figures out how to make the robots break down, so "just one rule" (anarcho-pacifism) becomes "no rules", which pretty much fits the "chaos" definition. It's not pretty.
The science fiction novella Anarchaos by Donald E. Westlake plays this trope utterly straight, as the title would imply. He posits a world entirely colonized by anarchists, which breaks down within a single generation into, well, chaos (in the story the world is named Anarchaos by the anarchists themselves, which seems unlikely). Overall it comes off as Westlake having a dislike of anarchism that he's trying to get out with an Author Tract, but despite that it's a good story.
Averted in The Dispossessed by Ursula K Leguin. Much of the plot revolves around Shevek (the main character) fleeing his anarchist people because they've become too unchaotic, with an unofficial government firmly in charge.
Averted in Eric Frank Russell's short story "...And Then There Were None". In it, an anarchic-libertarian community of Gands (they derive the name from Mahatma Gandhi) is pretty orderly, and also utterly pacifistic-they employ passive resistance when the Earth military tries to coerce them.
Live Action Television
Star Trek: The Next Generation had the episode "Legacy" featuring the planet Turkana IV, which was the home of a failed Federation colony that had descended into civil war and then lawlessness of the kind generally associated with anarchy. This being Tasha Yar's home world, from which she'd escaped as a teenager, her sister Ishara Yar helped the crew of the Enterprise retrieve two Federation officers whose escape pod had crashed in the ruins of the colony. While things were no longer so chaotic as Tasha had previously described them, Ishara's explanation for this was that the failing government had adopted the two largest political factions known as the Alliance and the Coalition as its emergency police forces, which backfired spectacularly, leaving them fighting over power. From a certain point of view, their violent lives in these two factions' underground strongholds were a slight improvement over the utter lawlessness that prevailed in Tasha's time, when rape gangs roamed the ruins of the city preying on any victims they could find.
The narrator of the Sex Pistols' most famous hit, "Anarchy in the U.K.", appears to hold no political affiliations, and desires nothing more than a chance to channel his baseless anger into mindless violence.
Elite features star systems with different government classifications, one of which is Anarchy. Anarchic systems tend to be the most infested with Space Pirates out of all of them.
As hinted at in Call of Duty: Black Ops 2 and elaborated on in the short story Rightful King, ultimately Raul Menendez is an Anarchist in the traditional sense of the word; he's against both big government and big capitalism, with the motto of "less power, less problems". Ironically being a wealthy man himself he is part of the so called 1% that the 99% seeks to overthrow, a good deal of his plan being funded by drug money. If the man does want change, It's certainly not change we can believe in.
In the webcomic series S.S.D.D, the part of the timeline set in the future features (among other super-governments) the Anarchist Collective, which sort of goes back and forth. Officially, there are only two laws, "do not profit at the expense of another anarchist" (which can be interpreted to cover anything from scams to murder), and "there are no other laws". The officials in charge are referred to as "Advisers" who don't put out laws so much as "suggestions"; you can technically break them without any sort of official penalty, but since the only difference between local police, angry crowd and lynch mob is how organized they are... the Collective does have a rather intimidating military, not to mention a secret weapon, though.
There's also a reference to "true anarchists" who live in the wasteland between cities, taking potshots at passing vehicles.
Played with in The Legend of Korra. The villain Zaheer believes in a philosophy that is very much like anarchism. He sees that people will never be truly free until all governments have been brought down. When confronted with the fact that this would lead to chaos, he is okay with that since he sees the natural order as disorder. The extensive riots and looting that grip Ba Sing Se immediately after the assasination of the Earth Queen prove that, yes, eliminating a leader like that will indeed plunge a kingdom into chaos.
in Adventure Time the brief moment when the goblins don't have a King turns into this.