A weapon used as a deterrent, to sway people into acting in a certain manner. This comes from the second moral of the original story of the Sword of Damocles, where "The value of the sword is not that it falls, but rather, that it hangs."
More often than not, the weapon is intended to have some type of height advantage, to more explicitly invoke this image. This can include launchable weapons that once off the ground serve that purpose.
The Kill Sat may easily be an example of this. The Weapon for Intimidation is a somewhat related, smaller scale version. See also Gunboat Diplomacy.
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Nationwide Insurance has a commercial where a woman's insurance deductible hangs over her head as a giant rock in a net, threatening her much like the titular Sword. ("The World's Greatest Spokesperson in the World" is able to make it shrink with Nationwide's "vanishing deductible".)
In One Piece, the protection or threat of some of the Three Great Powers is used to control specific locations. Whitebeard's protection kept people from attacking even the weakest of his territories, Boa Hancock's membership in the Shichibukai protected her home of Amazon Lily, and the threat of a Marine Admiral, Buster Call, etc., kept certain laws and policies in place for the marines.
The Three Great Powers are more of a delicately balanced Cold War. The deterrent is their respective strengths. The Buster Call would fit with this trope more, though there is no one weapon in the series yet that keeps any sort of peace. On a smaller scale, things are protected using the threat of powerful individuals.
The World Government and at least one other independent villain have tried and so far failed to acquire a truer version of this trope in the form of one of the three Ancient Weapons. The World Government are convinced that with an ancient weapon at their disposal, they'll be able to end the age of piracy (and any other opposition to their rule). Said independent villain was also confident that the World Government would let him get away with anything once he had attained the weapon Pluton.
In Castle In The Sky, Muska takes control of Laputa for just this reason.
In Soul Eater, Arachnophobia get their hands on an Artifact of Doom named Brew, but it doesn't work (because Medusa's team stole the real one and gave them a fake). However, Arachne still realizes it to be useful because everyone thinks they have it, and thus can still threaten enemies into retreating.
Literal example — the first episode of K has two massive swords hanging in mid-air, one of which is referred to as the "Sword of Damocles".
In Watchmen, Nite-Owl's Archimedes seemed to be intended to serve this purpose, and was used this way when there were riots in the streets. Though, as it was his ship, it wasn't exactly taken seriously.
This is also Ozymandias's plan — by creating fear of an extraterrestial attack, he intends to scare the planet into world peace. It seems to work, but close examination reveals he launched his plan just as the United States and the Soviet Union were about to start peace accords anyway, meaning that he's scuttled real peace in favor of peace based on a false fear, liable to collapse if it's ever revealed... like what may be happening a few days after the last panel.
In Like Flint. Gen. Carter schemes to load a space station with nuclear bombs instead of a weather laboratory (under the code name Project Damocles) and launch it into orbit around Earth.
One of the songs in The Rocky Horror Picture Show is titled "The Sword Of Damocles". In said song, Rocky sings about how he's just been born and how he can already fear that something is about to go terribly wrong.
Rocky: (Singing) The Sword Of Damocles is hanging over my head. And, I've got the feeling someone's gonna be cuttin' the thread.
In Star Wars, this is what Tarkin intended the Death Star and its superlaser to be used for: The threat of having your planet instantly destroyed would (presumably) curtail the ambitions of any seditious systems and work more efficiently than actually physically oppressing someone by force. The Expanded Universe gave this philosophy the name "The Tarkin Doctrine", and revealed that The Empire built an impractically large number of various planet-destroying devices in an attempt to implement it in practice. Since they all had a nasty tendency to get hijacked or blow up due to Rebel Scum, sabotage, or other unfortunate circumstances, the doctrine was a resounding failure.
In Austin Powers: Goldmember, this is the intended effect of Preparation H.
The evil professor from Real Genius makes his genius students build him a laser (while his Butt Monkey student/valet works on the tracking system) for a space-laser version of one of these he promised to the military (for a supposedly obscene amount of money).
Tony Stark's exposition of his Jericho Missile in Iron Man might be a variation of this; a weapon that only needs to be fired once.
Tony Stark: They say that the best weapon is the one that you never have to fire. I respectfully disagree! I prefer the weapon you only have to fire once. That's how Dad did it, that's how America does it... and it's worked out pretty well so far. Find an excuse to let one of these off the chain, and I personally guarantee you the bad guys won't even want to come out of their caves.
In The Reveal at the end of The Day the Earth Stood Still (1951), Klaatu claims that this is why his people built Gort and other robots like him; the robots were purposely programmed to destroy Klaatu's planet if war ever started, preventing the species from ever doing so.
Robert A. Heinlein's Between Planets. The Circum-Terra space station has hundreds of nuclear missiles, enough to destroy any military force that threatened Federation control of Earth.
Referred to in The Dresden Files as the "Doom of Damocles." The "Doom" is applied to those the White Council believes to be just shy of irredeemable, and can summed up as "One strike and you're out." With "out" meaning, "beheaded by the Wardens."
Ghost Story reveals that Harry himself served as this for Chicago with a lot of the supernatural community. They found him so terrifying that most just didn't bother showing up.
Referenced in The Salvation War, when referring to Uriel. Considering what Uriel is capable of, even with tinfoil hats and cruise missiles to stop him, this is not surprising.
Voldemort in the Harry Potter series uses the werewolf Fenrir Greyback this way: do what he says or he'll send Greyback after your kids. As Lupin (who was himself bitten by Greyback as a child) puts it, "It's a threat that usually yields good results."
Mission of Honor: When Honor shows up at Haven to negotiate a peace treaty, her fleet of superdreadnoughts in orbit are referred to as "an infinitely polite sword of Damocles".
Live Action TV
Star Trek: The Original Series episode "Assignment Earth". The U.S. is about to launch an orbital nuclear warhead platform. Gary Seven's mission is to make it malfunction to scare other nations into not using them.
This was taken very literally in Power Rangers Zeo, where King Mondo dug up a "powerful but unstable" weapon called the Damacles Sword which he had buried centuries ago so he wouldn't be tempted to use it. (Apparently, the sword was a self-induced version of this Trope, which he broke after thinking he could defy it. As it turned out, he could not. Trying to fight the Rangers with it only resulted in him losing (and being the first Big Bad of the series to fall in combat to the Rangers, a very dubious honor).
The Older Than Feudalismtrope namer, of course. As you know, he was a courtier at the court of the tyrant Dionysius II of Syracuse (Sicily, Italy). When he praised the tyrant for being so fortunate, Dionysius decided to give him a lesson and offered him his throne. Damocles accepted, but the tyrant hung a big sword above the throne, held only by a single hair (of a horse's tail). Soon, Damocles didn't think anymore that Dionysius was so fortunate...
Dungeons & Dragons. The Forgotten Realms spell Blade of Doom causes a sword-like blade of force to come into existence over the target creature. When the target performs a specific act, the blade drops onto the target, damaging it.
The Book Of Vile Darkness has a few spells that answer the question of "why don't the commoners rebel against the evil empire?" pretty succinctly, including one that causes it to rain acid over an entire region for months.
In Final Fantasy XII, though not an actual weapon (unless you count living people as potential weapons), Basch Fon Ronsenburg is the Sword of Damocles Vayne put in place to Marquis Halim Ondore IV, having proclaimed him executed years ago when Vayne told him to. He even mentions the trope in dialogue upon discovering it.
In Sonic Adventure 2, the Eclipse Cannon was intended to serve as this. This is why it was only fired as an example. No point in Dr. Eggman ruling an empty planet, is there?
In Front Mission Evolved the main enemy is revealed to be a terrorist group known as The Sword of Damocles and they plan to use a orbital laser to keep the nations of the world under their thumb
At the end of the Ancient China chapter in Live A Live, Odi Wang Lee reveals he always has a pair of assassins living behind his throne, with orders to attack whenever they see fit. They're strong enough to kill him, and thus he must always remain on guard - this is how he stays strong enough to be a powerful martial artist. They also serve as a last line of defense when the Xin Shan Quan master wipes out Lee's inner circle.
Soul Calibur IV features "Critical Finishes", One-Hit KillFinishing Moves that can only be used when your opponent's Soul meter is empty and yours is full. Since the Soul meter empties through blocking, they are clearly meant to discourage excessive blocking and are not meant to be seriously used.
Ryse: Son of Rome has this in the form of a dagger, one that's standardly issued to every Roman officer. It has the picture of the titular Damocles on it, though in contrast to the actual legend Damocles was a Roman officer who was betrayed by his commanders in the middle of a battle. He came back to life after being killed, donned black armor and a white face mask stained with blood, and killed them. Roman officers keep the daggers on them as a reminder to treat their legionaries well and to be brave in battle, should the Black Centurion come to kill them as well.
The Elder Scrolls: The Demigod Vivec saved his (equally named) city from a moonlet tossed at it by an angry demon from space, by stopping it, frozen in time, about sixty feet aboveground. He then used it as one of these, by making sure his followers didn't stop worshipping: The rock would fall on them otherwise. However, certain dead-God-heart powered incidents later, Vivec was gone, and the rock had to be kept in place by a soul-burning machine, which later got torn up by an elf trying to save his lover. And thus, we get to see the downside to the Sword of Damocles method: Eventually, the string gives away, and the sword must fall. In this case, with continent-wrecking results, as it resumed its fall like it had never stopped, turned the city into a boiling crater (and yes, it's still boiling centuries later), and set off the local supervolcano.
Xykon discusses this in The Order of the Stick prequel Start of Darkness; he would only have to unleash the Snarl once or twice as part of his bid for world domination, and fear of the Snarl would keep anyone from opposing him ever again.
A bit of Viewers Are Geniuses in Justice League: Project Cadmus employs "Damocles Class Missiles", which were used to fire directly into the space based Watchtower of the League to preemptively start a war between superhumans. The use of them is explicitly because Cadmus could not trust the league to continue to protect the people of the world.
In a different episode, Vandal Savage attempted to use a space based rail gun to aid his world domination.
Earlier, it is revealed that Silas was discharged from the military for creating Damocles.
Mutually Assured Destruction. Advances in weapons technology, such as nuclear weapons, were supposed to bring about an end to armed conflict in the traditional sense. It...well...KINDA worked...
International relations studies term this the stability-instability paradox. The fact that both sides have the ability to utterly annihilate one other severely limits the plausbile range of actions both sides can do in international diplomacy. On one hand, it means no World War III because the big powers won't make moves with the intent to go to war (it is assumed that both sides value their own survival more than they do the destruction of the other). On the other hand, this same system means both sides find less direct ways to fight the other side (i.e., via proxy wars with third and fourth parties).