Let's talk about some examples.
DnD's Amulet of the Planes
Amulet of the Planes is an artefact that lets you transport yourself and nearby creatures to another Plane of Existence you know. If you fail a roll, everyone gets scattered across that Plane and possibly every other Plane. So basically you have a pocket device from Sliders with notable chance to scatter the entire party across the multiverse each time you use it.
It is a powerful artefact, but one with a pretty high chance of throwing en entire adventure haywire. So either you make the point of avoiding using it, figure a way around its limitations, or YOLO it and ravel in the chaos to the GM's dismay. It's not really the type of artefact you just go "oh cool" and forget on your inventory sheet.
Taking20 listing Amulet of the Planes as a campaign-breaking item"It doesn't matter what your campaign was about, it is now a plane-hopping campaign"
Exalted's Dragon Kings
In Exalted there is an old race of creatures called the Dragon Kings. They are creatures of perfect resurrection - their souls retain the memories of all of their previous lives when they are reborn. Couple that with them being one of the most ancient races of the setting and being heavily intertwined with the highest deity of the setting and his Exalted heroes, introducing a Dragon King into the game opens up a large can of worms.
First of all, they have been around when the land was ruled by titans and a lot of them would probably have first-hand experience of their cruelty and how the world was put together. This history goes strongly against the cosmology put forth by the biggest faction of the setting, the Realm, but also many other players like Autochtonia, etc. They have dangerous knowledge.
Secondly, they've lived through multiple apocalypses and many of them could know of a number of ancient tombs filled with treasure and weapons from the height of the Deliberative. If anyone would know where some mad warmonger keeps their stash of doomsday weapons, it would be these guys.
Thirdly, depending on how you play them, they might be a terrible influence on some of the Exalts, particularly Solars. Our GM likes to portray them as sycophants, and there is no easier way of making a character do horrible things than to inflate their ego with flattery and tales of how they once were the rulers of the world. If their word was law and they could do no wrong, how can this time be different? They deserve to subjugate their enemies after all...
During the Congenials Season 1 Episode 7 our GM introduced a ghost of one of the Dragon Kings as a story hook for one of the players and it absorbed most of the attention from the party. The Solar wanted to cleanse its soul right there and then, the Alchemical wanted to extract the heretical history out of their head and mess with its reincarnation so they'd have a knowledgeable companion, and the Dragon King wanted to whisper honeyed words into the Solar's ear. That character alone sparked a large deal of debates for the players, both in character and out.
SWN's True AI
In Stars Without Number Revised the players can choose from a few key character classes - Warrior, Expert or Psychic. These are all pretty standard and pretty balanced between one another. However, in the Deluxe edition, you can also pick a fourth option - to play a True AI.
In SWN, a True AI is not just a normal robot like R2D2 or C-3PO (that would be a Virtual Intelligence character "race"). A True AI is Ultron:
True AI in a nutshell
Straight away at character creation you can take the murderbot frame (Omen) and be able to rip and tear way above your weight class and tear through even ship hulls:
This is your starting PC.
Yes, the one in the background that looks like
Michael Bay's Megatron
If you have a ship with the correct modifications, you can run it by yourself by level 2. If you had a hacker in your group, by level 3 they are outclassed by your innate hacking skills. At the same level you can control almost 3000 drones and it only gets crazier from here. By the time you're at level 9 you can teleport, rewind time, dictate how events will unfold in the future, and retcon almost any level of preparation out of your hat ("why yes, I did bury a spare spaceship with months of life support and power armour on this desert planet for this exact eventuality"), so you're outclassing a lot of psychics (oh, and unlike them, your powers can't be countered or detected by psychics).
All the while you have a lich-like phylactery which makes you a lot more immortal than anything in the universe, and you can swap your shells to get high bonuses to specific things ("need a medic? I can be a medic in 5 minutes. Need a mechanic? I can be one as well").
In-universe, the value of a True AI far exceeds what any player or even entire planets could earn, and they are also extremely dangerous if they turn malicious. Heck, in-fiction True AI have to have breaks on them to dumb them down to human-level thinking. Otherwise, these "unbreaked" AIs turn extinction-level-entity very rapidly.
So the moment a True AI gets introduced into the game, you're dealing with a large elephant that needs addressing. If it's a PC, they can make the game interesting very quickly (especially since SWN encourages the GMs not to "keep the PCs poor" and so on). If the PCs find a True AI, they can get either very rich, or very dead, depending on how things roll. Heck, RollPlay's SwanSong was a game about dealing with unbreaked AIs and the nightmare even one of them can be.
EvWoD's Ceasing to Exist Approach
In Exalted vs the World of Darkness Sidereals have a Charm called "Ceasing to Exist Approach". It lets your current self stop existing while you take on the life of any person you want, whether they are human or supernatural. The past reweaves your new existence into itself to fit you, so if you are a vampire prince's daughter you have the backstory to back it rather than appear out of thin air. You also get a lot of dots in Backgrounds, meaning you can have a lot of potential influence as a character - you could be a high-ranking member of the vampiric society and a millionaire at the same time, etc.
The thing is, when you end this power and go back to being yourself, that other story doesn't vanish, just the person goes missing. Suddenly the prince's daughter is missing, or a politician is nowhere to be seen, or what have you. Their stuff is also there, and since you know their bank account passwords or could arrange some other transfer to your old self, you can bootstrap a lot of interesting stuff to yourself. You could for a moment create a Bruce Wayne-like figure in your town, complete with an Alfred, tell them what's going on, then come in as yourself and enjoy your life of luxury and a hyper-competent and loyal butler.
So the Charm is very powerful, but also has strong drawbacks that have vague consequences. You could use it to bypass a lot of problems ("our target is locked up in his doomsday bunker? Good thing he was his loyal butler by his side! Disappears!"), which can make the game a bit boring and very frustrating for the GM. It's also a very expensive Charm, so it's a Plot Elephant - either the game is about hopping identities and you make the investment, or you just spend a good chunk of XP on something you don't want to use or can't utilise.
Sidereals Ceasing to Exist everywhere...
When introducing elements into your game that are very strong, have a lot of knowledge to share, or have the chance to derail the plot, you should be prepared for what you're getting into. Once a Plot Elephant is in the game, your whole game could revolve around it, or be shaped by it. This of course can make for some excellent stories and even entire games, but if they weren't meant to be the focus, they can take away from everyone's enjoyment. Teleporting someone into the Elemental Plane of Fire might be a fun joke once and getting your party back together from across the multiverse might be an interesting story, but both can be frustrating the second and third time around...
Respect and acknowledge the elephant in the room...