The Time of Myths was a dangerous age to live in, with Eldritch Abominations on the loose, evil gods eating souls and whatnot. So it's not surprising that after becoming Sufficiently Advanced, the Precursors made superweapons to defend themselves and make the galaxy or planet a safer place for their descendants. Conscientious precursors will dismantle or at least disable these weapons while preserving them for later use — usually by scattering the component Mac Guffins across the cosmos or placing some kind of condition for activation (say Virgin Power, or innocence).
Of course, most precursors tend to be either neglectful or outright abusive. What this means is that they will make these superweapons for no particular reason other than that they can. And even Benevolent Precursors might have rogue elements or simply have their superweapons seemingly destroyed and thought lost amid the casualties but in fact thrown through time. The weapon itself may have had legitimate use once upon a time, but after making the planet destroying espresso machine to defeat Somnus the Snorer of Worlds, they will completely forget about ever having made it and leave it in an easily accessible location. The device will (of course) be immune to the ravages of time and ready to use minutes after being found. Worse, the precursors may not have even labeled the thing! So for all intents and purposes it seems like a normal espresso machine... which will destroy whatever planet it's on after one use. Of course, every villain or misguided soul in the setting will do whatever it takes to possess and activate the device, sometimes without even realizing (or underestimating) the danger it poses.
Alternatively, it represents something powerful with great potential for abuse that is knowingly left behind. Lastly, it can also include examples of Sealed Evil in a Can where the evil could easily have been defeated, but wasn't for no good reason, forcing people to deal with an unrepentant and now further insane monster in the future.
It's as if the the US and Russia decided to "get rid" of all their nukes by putting rune encrusted marble doors outside every missile silo and left it at that. Oh, and the runes spell out "Come in, there's punch and cake! Just turn both keys at the same time".
Not to be confused with the "plain" Doomsday Device.
Examples:
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Anime & Manga
In Slayers, the elves created a powerful weapon that is immune to all magical attacks. It could also spit out smaller duplicates. Unfortunately since the artifact is immune to all magic, it cannot be controlled. So, the elves just buried it and hope no one will ever find it.
Comic Books
Doomsday itself. He is created on prehistoric Krypton with the sole purpose to destroy all life with an absurd amount of brute strength to back it up.
The Ultimate Nullifier is a device that can disintegrate anything (and sometimes more than that, depending on the continuity)—up to and including the entire universe. It's been used to stand off Galactus, but it's not at all clear why the thing exists in the first place, or why it's kept in Galactus' starbase.
It's actually a part of Galactus himself.
Film
In the So Bad, It's Good movie Puma Man, the artifact in question is a mask that can control minds. This mask was designed by a race of Sufficiently Advanced Aliens who believe that "Each man is a god, each man is free." This mask has no purpose other than to steal people's will, it can even be used to force people to commit suicide.
Plan 9 from Outer Space: The aliens' motivation for (ineffectively) terrorising Earth is because they believe if humans continue to advance, we'll create exploding sunlight that will cascade-detonate the universe.
In the Stargate setting, the Ancients seemed to make a hobby of building these. Prominent examples include:
the Dakara Superweapon: capable of selectively disintegrating throughout the entire galaxy a particular species of life or all life in general, depending on how you set its incomprehensible but easily-used controls. Originally built to stop a plague and re-seed the galaxy with life.
the San Graal: capable of destroying all Ascended beings in a galaxy — granted, this one was actually intended to be a weapon, and deliberately hidden behind puzzles.
Actually, it was instructions to MAKE the San Graal, and the good guys were given some assistance to find it, so this may be more of a conscientous precursor than Pointless Doomsday Device.
the Asuran Replicators: a form of machine life built as a weapon to destroy the Wraith but then abandoned to its own devices when it proved to be a "failure" in some undefined way. The Ancients at least did try to destroy it, but of course didn't do a particularly thorough job.
Actually they did do a pretty thorough job, unfortunately out of the uncountable trillions of nanobots that make the Asuran Replicators they missed a couple, which was all that was needed to rebuild themselves.
They are called Replicators for a reason, and these are the Ancients we are talking about. They can seed/destroy all life in a galaxy. They build a ship that automatically travels around the universe planting Stargates. Thorough would have been to alter the planet's orbit so it crashes into the sun.
Project Arcturus, an attempt to build a super-powerful power source that turned out to be highly unstable and that emitted unstoppable deadly radiation when in operation. Killed everyone on the planet with its radiation, but they left it in place for future tinkerers to mess with (and eventually wound up exploding, destroying 5/6 of the solar system it was in)
After the original blew up, the Atlantis crew revisited the concept, and this time almost managed to destroy a parallel universe. Apparently they were fast learners.
It wasn't that it emitted deadly radiation: it was that it emitted ENERGY. Uncontrollable levels of energy, which resulted in the weapon firing on everythng within a line-of-sight from it, devastating the planetary colony just as much as it did the Wraith fleet in orbit of the planet.
The Ancients were losing the war against the Wraiths and were desperate for any weapon that could turn the tide. However, as the Wraith attacked Ancient worlds, the Ancients had to abandon most of the research and prototypes. Since they were convinced that they would eventually win and reclaim all that they lost, they did not bother destroying or neutralizing all those DoomsdayDevices. During the final evacuation from Atlantis they even left a functioning time travel device behind.
Not to mention, you know, Atlantis. Which given the chair platform, super shields, and the Ancient database, probably qualifies as a whole squadron of doomsday devices, at the very least.
A weapon used for destroying Stargates. It can be used to maintain a wormhole indefinitely (Beyond the 38 minute limit), but doing so causes the gate on the otherside to eventually overload and explode, taking most of the planet with it.
The Altero device, which was specifically tuned to Wraith hyperdrives to cause them to blow up during a jump throughout the galaxy. Unfortunately, it had the nasty side effect of causing every active stargate to explode in a planet-busting manner. Whoops! To their credit, they have actually hidden the lab fairly well.
Once the Ancients ascended they stopped caring about all the deadly technology they left behind and regarded any attempts to fix this as forbidden interference with non-ascended beings.
The Ancients came up with a lot of ideas for good technology. Unfortunately, most of it didn't work as intended and had extremely dangerous side-effects. Not only did they leave these devices lying around, but they didn't slap any sort of warning label on them, either. Example: A machine that helps the user ascend in a matter of days. Downside: Failing to ascend in a matter of days after using the device is fatal, and ascending this way ain't exactly easy.
The planet-eating "doomsday machine" that appears in an episode of Star Trek: The Original Series seems to be one of these. Kirk can only guess as to where it may have come from or why it was activated, but he still has to stop it before it destroys anything else.
His guess is that it was built for an ancient war that neither side survived after it was activated. If true the trope wouldn't apply, since it wasn't forgotten so much as it just kind of wandered off while still in use.
Peter David's TNG novel Vendetta expands on the doomsday machine: It was built as a last-ditch weapon by a race which had been nearly wiped out by The Borg. The one that Kirk destroyed was on an automated course, not to Earth, but through Earth to get to Borg territory.
Literature
Larry Niven's Known Space novels and short stories have one of these in the distant background, a device which supposedly ended the "Slaver Wars" and left fragmentary populations of survivors to survive into the distant future.
The Star Wars Expanded Universe features the Shawken Device, which is supposed to destroy the universe. It is notable for operating on principles that are considered dubious at best even by characters in the comic book in which it appears. But nobody really wants to test it, just in case. Luke and his sort-of apprentice even go to great lengths to disable it.
Also from the Star Wars EU is Centerpoint Station, a massive space station with the power to both move and destroy celestial bodies. Built by a ancient race called the Celestials, it doesn't seem to serve a purpose besides being a handy superweapon for the plot. Until Fate of the Jedi revealed it Sealed Evil in a Can... Or rather, it was effectively a gun pointed at the Can that was supposed to go off should the Sealed Evil escape. Too bad the heroes blew it up in the previous story arc.
The Hypernova Bomb created by Hactar, and "given" to the Elders of Krikkit, in Life, the Universe and Everything. Hactar was original designed and built by the Silastic Armorfiends of Striterax and tasked with creating them an Ultimate Weapon. On asking what they meant, it was instructed to "read a bloody dictionary". Whilst indeed pointless (it would blow up the entire Universe, leaving no victors but indeed making it the last weapon ever) it was a nice example of how the customer may be stupid but they are never wrong.
In the third Empire From The Ashes book, the Fourth Empire's plans for an extremely-advanced gravitronic bomb capable of destroying a sun—all on its own—are discovered. By this time, the Fifth Empire is already well on its way to restoring its military might to the Achuultani-raping levels of the Fourth (with centuries to spare), so there's really nothing else to do with the plans besides let them fall into the hands of a highly-organized, widespread group of religious terrorists bent on toppling the government for allying with the minions of the Anti Christ!
The "bio-weapon" of the Fourth Empire probably qualifies for when it was invented, as well. No amount of paranoia over the yet-unseen wave of genocidal invaders can make other than mindbogglingly insane the creation of a rapidly-evolving super plague that destroys all life, has a very long dormancy period, and cannot be cured. That it turns out they could have effortlessly wiped out the invaders with their current military power just makes things worse.
Possibly the Time Matrix from Animorphs. In The Andalite Chronicles, it was implied to have been created by the Ellimist(s), the theory being that he/they used it to Ascend to a Higher Plane of Existence in the first place. Years and dozens of books later The Ellimist Chronicles told the real story of how this happened, and the Time Matrix didn't even get a mention. So, who knows?
There is a bit of justification for it just being left behind, though—neither the Ellimist nor Crayak want the other's side to have it, so their "game" presumably has a rule about neither messing with it (until they had to in Elfangor's Secret). Still leaves its origin (and how it got on Earth before the Skrit Na found it) a mystery.
Played with in Warhammer 40,000. Finding ancient doomsday weapons with no clear purpose evident is pretty common, but the setting being what it is, pretty much all of them did have a purpose at one point in time. The Blackstone Fortresses, for example, seemed pointless until the Necrons, whom the Fortresses were built to combat, returned.
Boatmurdered's FTW is more an example of a standard Doomsday Device, in that it was used repeatedly and to great effect protecting the fortress from everything from goblin invasions to Bronze Colossi to unfortunate merchant caravans who arrived at just the wrong time. The fact that it ultimately lead to the firey downfall of the settlement is more a tribute to its epic mismanagement.
Best of all, succession games incorporate the "Lost Technology" aspect of the trope — within real-time days or weeks, as one player constructs such a device and connects levers to it, but then doesn't label any of the levers so that a few players later, somebody inherits it and literally has a) no idea how to activate the device if they wanted to and b) no idea which lever does what. The results are pretty much inevitable, especially given that tantruming dwarves often throw levers without being ordered to.
Boatmurdered also featured a lever to flood the siege workshop. None of the players could remember why (the room had formerly contained a farm plot).
Headshoots had one hilarious example; a failsafe switch for WEAPON is right next to and the same colour as a device that releases all the cats from a cage.
So saving the world involves killing your framerate?
It used to be (It still is to a lesser degree) that anything caught under a closing drawbridge would be utterly destroyed, removed from the game. This was refered to as the Dwarven Atom Smasher, and was useful for everything from destroying enemy seiges to getting rid of garbage.
Check out the community pages (The forums and the wiki) for plenty more examples. Most notably, the wiki offers a suggestion that players build a 'doomsday clock'; a mechanism that will, if a certain pressure plate is not triggered for X amount of time or some other condition is not met, destroy the fortress and render it permanently uninhabitable.
The succession game famous as Boatmurdered 2010 Battlefailed had FAILCANNON similar to FTW but was designed so that the faucet was a giant skull. It lived up to its name at first, after reclaiming the fortress they rebuilt FAILCANNON and are currently testing it as we type this
Just whom did the Precursors of Star Control have to deal with that warranted the fleet buster that was the Sa-Matra? And why would they leave it behind when they left the Galaxy?
Well, we know the planet-busting bombs that was used to destroy it were engineering tools ...
And it is arguable whether they left the Galaxy at all. The device may have been intended for use to fix "mistakes" (like the Mycon and Daktaklakpak).
The Ultima series has the Armageddon spell, which will wipe out all life in the universe. (except Lord British, and sometimes the caster is immune too. Sometimes.) In Ultima VI, you're given the spell as a freebie by the Xorinite, hoping to entice you into taking advantage of their information-brokering services. They don't think the spell is very impressive since it only affects the current plane of existence.
Played with in Tales Of Symphonia and Tales of Phantasia. The superweapon, the Mana Cannon, wasn't left behind- the plans were. Despite the weapon ultimately being the destruction of every society to use those plans, its one of the first things to be built when magitechnology rebuilds from the inevitable knocked-back-to-the-stone-age that always follows its construction. Except in Symphonia, where it didn't destroy the world — but proved mostly useless in saving it too.
In Fallout, The Cathedral's basement has a fully functional atom bomb that can only be used to destroy the Cathedral. Just in case The Master decides his Master Plan is flawed beyond salvation and just wants to end it all instead of finding a new plan, or telling the people working for him. Also very convenient if some aspiring person with technical knowhow happens to disagree with the Master Plan and makes an unannounced visit.
Final Fantasy X-2 has Vegnagun. It is a powerful superweapon, yes, and would probably be actually quite useful — if it didn't destroy the entire world upon firing.
If fired up at the roof of an underground cavern, then yes it will blow the surface above to smithereens. Presumably that is not how it was meant to be used. The reason it's sealed away is because it has a broken IFF.
