In General, every format has at least one deck that qualifies as Game Breaker. The Gamebreaking deck and cards in Yu-Gi-Oh! constantly change whenever the metagame shifts, new cards are released, and the Banlist is shuffled. As a general rule of thumb, cards that are placed on the banlist were found to be broken at the previous format. Also, as a result of Sequel Escalation, some old decks that were completely unfair in their heyday would be not be so great a threat nowadays, even if they're untouched by the banlist. A good example of this was the old school Beatdown deck with some equips. Back in the day, it was THE winning deck, but since then it's become obsolete.
To elaborate, in the old days, all one needed to do was summon a Cyber-Stein to ensure victory. Cyber-Stein on its own is not that great - terrible attack and defense, practically useless, right? Wrong. It has a nasty little effect that lets you summon a fusion monster at the cost of 5000 life points. ANY fusion monster. Like, say, a Blue-Eyes Ultimate Dragon, with 4500 attack, for instance. Using this effect almost ensures you have less life points than your opponent, which allows you to equip Megamorph (doubling its attack to 9000) and Fairy Meteor Crush (allowing it to deal damage to defending monsters) to it and attack for game. Arguably considered to be the first One Turn Kill ever invented in the metagame, since life points started at 8000. When the card was introduced to America, guess how long it took for it to be Forbidden. However, in time, something even worse replaced it, and this force would change the history of the game forever. And that was...
The Envoys. Good God, The Envoys. These cards, when used in tandem with a certain other monster i.e. Yata-Garasu, are the very reason that the Forbidden / Limited list exists today. Their abilities are so ridiculously overpowered that, for a long time, they completely dominated the metagame. If you were not using a deck that utilized these, your chances of winning dropped by 90%. This list is used to cull combos that create win conditions other than "attack until your opponent dies."
Black Luster Soldier: Envoy of the Beginning is easily Special Summoned by removing a LIGHT and a DARK monster from your Graveyard, has high Attack, and can either 1) remove one of your opponent's monsters from the game at the expense of not being able to declare an attack that turn, or 2) attack twice in one turn (if the first attack destroyed a monster). It was banned for many years until Konami, seeing new potential for brokenness with Xyz Monsters, gave it a second chance and made it Limited to only 1 per deck.
Chaos Emperor Dragon: Envoy of the End is Summoned in the same way, has equal ATK, and has an effect which requires its controller to pay 1000 Life Points, but 1) sends every card in both player's hands and on the field to the Graveyard, and 2) does 300 damage to your opponent for each card that gets sent to the Graveyard by this effect. This generally ended games. If it didn't, then something much worse awaited that ensured all hope was lost...
Yata-Garasu, which is quite possibly the most broken card in all of Yu-Gi-Oh!, period. What does this little black bird do? If it damages your opponent, they must skip their draw next turn, which means that they get no new cards to have any chance to do anything. It also leaps back to the summoner's hand at the end of each turn, making it difficult to remove from the game. This means that if they have no summonable monsters in their hand, youwin. This card made decks with more than three or four monsters that required sacrifices suicide, and forced dramatic changes in tactics if you even thought your opponent's deck contained it.
Last Turn, which clears the field of all but one of your monsters, wipes the field and hands and then your opponent special summons any monster, last man standing wins. Sounds fair right? Until you realise just how many monsters have an effect that prevents special summons...
Some Synchro monsters have reached this level; the requirements needed to summon them (a Tuner and non-Tuner monsters, whose levels add up to the level of the Synchro Monster) work insanely well with popular aggro-swarm tactics, making them staple cards in almost all decks. Key offenders include:
Dark Strike Fighter, a level 7 monster that can sacrifice monsters to deal damage equal to their Level x200. Sounds simple? A direct attack from this card plus its own effect does damage equal to half of your Life Points. Which means if you'd taken a bit of damage already (or there were other monsters to attack and sacrifice), this "finisher" ended games on the second or third turn. The worst part was that it was an inverted Nerf from the anime that removed the factors that would have made it balanced: the effect only being allowed once per turn, preventing it from attacking on the same turn, and that it could not sacrifice itself for its effect.
Goyo Guardian, a level 6 monster that can steal any monster it runs over. It was Summoned easily and repeatedly in Synchro Cat decks and has 2800 Attack. For a comparison, after it was banned, Gaia Knight, the Force of Earth replaced it. Gaia Knight has 2600 Attack. Gaia Knight is used for nothing except really high ATK.
Brionac, Dragon of the Ice Barrier, a level 6 monster. You can discard any number of cards to return that many cards on the field to the hand. This eliminates your opponent's Trap defense while setting up the Graveyard. Also, since Synchro, Fusion and Xyz monsters can't exist in the hand, you can make them disappear into the Extra Deck. Brionac has been used to bounce cards in the player's own possession, most notably Premature Burial, leading to Graveyard revival abuse, and banning of that card as well.
TRISHULA (Also known as Trishula, Dragon of the Ice Barrier). Okay, maybe it's level 9 and needs two non-Tuner monsters, so it's hard to summon at first sight. But it's very easy in practice, since many Tuners summon non-Tuners automatically and Special Summons are frequent in the metagame. Its effect: it removes one card from your opponent's field, one card chosen at random from his/her hand, and one from his/her Graveyard when you summon it. During the days when you could use three copies of it, you could summon one after another, burn your opponent's cards before they could even play them, and attack with impunity. It was extremely powerful in Infernity where the player could negate anything the opponent threw out to stop Trishula's effect combined with their perfectly placed engine to summon Trishula.
Mist Wurm later replaced both Brionac and Trishula once they hit the banlist. It's a Level 9 Synchro Monster that is essentially both of them combined. When summoned, this thing sends 3 cards on the opponent's side of the field back to their hand. When combined with something like Lightsworns, Blackwings, or anything that can swarm the field with powerful monsters, it usually results in an OTK.
T.G. Hyper Librarian, a Level 5 monster that lets you draw when a Synchro Summon happens. Most players would use the newly drawn cards to make more Synchro Monsters, and draw, and so on. For the few months it was Unlimited, it was stupidly powerful. In a swarmy-Synchro Deck, it was not uncommon to see two on the field at once. And let's not get started on Formula Synchron, a Level 2 Synchro Tuner Monster that lets you draw a card when it hits the field. 2 Librarians plus 1 Formula would net you 3 cards, and then you could Synchro Summon...
Shooting Quasar Dragon, pretty much the ultimate Synchro Monster. First of all, it can negate any effect other than a counter trap once per turn. Second, it gets an attack for each non-Tuner Material used in its summon—with 2 attacks at 4000 ATK, it can end the game by itself. Third, if you somehow manage to get it off the field, it would special summon Shooting Star Dragon, another Synchro Monster with 3300 ATK, the ability to negate destruction once a turn, and up to 5 attacks.
Any Tuners that special summon other monsters from the deck or graveyard, like Chaos-End Master, make Synchro Summons a lot easier to pull off, but Deep-Sea Diva takes the cake. To elaborate, when Diva is Normal Summoned, easy to pull off since it's a Level 2 monster, It can Special Summon a Level 3 or lower Sea-Serpent monster from the owner's hand or Deck. It may not seem that great at first, allowing for only a Level 5 or lower synchro summon by itselfnote Which is already practical on its own, allowing you to summon T.G Hyper Librarian or Ally of Justice Catastor, when having another monster on the field, you can easily pull a higher level synchro summon with Diva. Among the many possibilities of Synchro Summons you could pull off with this, you can use Diva's effect to summon another Diva while you have a Red Dragon Archfiend on the field to summon Red Nova Dragon, or use it to summon a level 3 Non-Tuner while you have a level 4 monster on the field to easily summon TRISHULA described above.
Before its key cards were banned, Frog Driver was a reliable first-turn-kill deck. It relied on:
Mass Driver, a Continuous Spell Card which can sacrifice a monster to inflict 400 damage (1/20 of a player's starting Life Points),
Substitoad, which can sacrifice any monster to summon a Frog monster from your deck, as many times as you want,
Ronintoad, which can summon itself from the Graveyard as many times as you want as long as you remove a Frog monster from the Graveyard,
and Swap Frog, which can Special Summon itself, dump Ronintoadin to the Graveyard, and serve as the first sacrifice for Substitoad. The deck wins by using Substitoad to send about 20 Frog monsters to the graveyard, and looping Mass Driver with Ronintoad to do 8000 damage and win. Mass Driver has quite a few instant-win combos off of infinite summon loops, but none are as consistent as this.
Blackwings used to dominate, with oodles of support, the ability to Special Summon many times in a turn, and quick recovery via Black Whirlwind and Dark Armed Dragon. They were particularly good at making Dark Strike Fighter and using Vayu the Emblem of Honor to win out of nowhere. About half of their key cards are now on the Forbidden/Limited List.
Lightsworns. Many of them have simple, strong effects, but force you to send cards from your Deck to your Graveyard. This is less of a drawback than it seems—it's much easier to revive monsters from the Graveyard than to recruit them from the Deck (some, like Wulf, Lightsworn Beast, revive themselves), and support cards like Lumina, Lightsworn Summoner and Beckoning Light can use the Graveyard as an extra Hand. The archetype's trump card, Judgment Dragon, has 3000 ATK, is Summoned when you have 4 or more different Lightsworns in the Graveyard, and can nuke everything else on the field for low cost.
The engine's starting core consists of Charge of the Light Brigade, which mills 3 cards and adds a level 4 or lower Lightsworn to your hand, and Lumina, Lightsworn Summoner, who mills 3 cards at the End Phase and can discard a card to revive a level 4 or lower Lightsworn. Since certain support cards only work in the Graveyard, you can use Lumina to turn a useless draw into a 2100 attacker. Or dump Plaguespreader Zombie, revive it by its own effect, and Synchro for Trishula. Or revive Garoth, Lightsworn Warrior and draw free cards in the End Phase. Or...you get the point.
Also used in the Deck is Honest, a Game Breaker on its own merits. Discard him from your hand to allow any Light monster (the LIGH Tsworns are Light) to gain the Attack points of a monster it's fighting until the end of the turn. Because it activates in the hand and has a specific timing that dodges most defensive cards, you are pretty much guaranteed to overpower any monster. On top of that, Honest can be returned from the field to the hand to dodge Judgment Dragon's effect and can be added to the hand via Beckoning Light to rig your hand with every Honest used or milled so far. Back when you could use more than 1, you could win any battle AND inflict massive damage no matter what monster you were using. This is often combined with Necro Gardna, a Dark monster capable of removing itself from the Graveyard to negate an attack to make a massive wall of defense.
In addition, the Lightsworn mill mechanic gives you immediate access to engines that rely on the Graveyard. And there are quite a few. Most notable are the Plant engine, which gives you free Tuners for Synchro and Tribute Summons, the Zombie engine, which uses Mezuki and Zombie Master to repeatedly revive Zombie Tuners for quick Synchros, and the Chaos cards (easily splashed in since many Staple monsters are DARK) to clear out enemy fields and act as quick Synchro fodder. The Zombie-sworn deck dominated a banlist format, receiving a comprehensive Limiting on the new banlist.
Dark Armed Dragon was Envoy of the Beginning Part Deux. Sure, it requires EXACTLY 3 Dark Monsters in the Graveyard, but that's easy with the Graveyard manipulation for DARK Monsters. Its effect lets you remove a DARK monster from your grave to destroy one card on the field, and it isn't restricted to a certain number of uses per turn. As long as you have the Darks, you can keep blowing things up, and with a 2800 body no less. And it's Special Summoned, meaning you can put down another monster in the same turn. DAD is the star of the many decks, and is commonly splashed into anything that has DARK monsters and Graveyard manipulation.
The Dark Armed Dragon deck that created the ban list discontinuity was DAD Return, the first deck to receive the honor of an emergency banlist. By removing powerful monster cards (e.g. Dark Magician of Chaos, who returns a used Spell Card to your hand when summoned) for the effect of Dark Armed Dragon and Allure of Darkness, you increase the number of monsters that will come back with Return from the Different Dimension/Dimension Fusion while speeding your approach toward drawing those cards. You then create a loop of powerful creatures by grabbing Fusion through DMOC's ability and continue until you win.
The Tele-DAD deck, starring DAD and Emergency Teleport, relies on card synergy, speed and explosive combos. This is achieved through its amazing draw power (Allure of Darkness and Destiny Draw) and hand/deck customization (Reinforcements of the Army, Plaguespreader Zombie, Emergency Teleport, Dark Grepher, and the old Destiny Heroes engine) since most of its key cards could be run in triple. The TeleDAD deck was so broken, literally NOTHING ELSE could compete. With a good TeleDAD deck, it was incredibly rare for games to last more than 3 turns. It is one of the two honorary holders of the title Tier 0, a title that was previously only held by the Chaos Deck, for which the ban-list was created, and is considered the better of the two since more counters were supposed to be available at this point. For a while, ONE copy cost upwards of $200. Yes, $200 for cardboard.
The Infernity cards. Sure, they have the drawback of requiring the player to have no hand to activate, but there are lots of ways to get rid of your hand in no time and the Infernities' effects are extremely powerful. The worst offenders are Infernity Mirage and Infernity Launcher, both of which can be 1-Card One Turn Kills.
The Infernities also inspired a special flavor of Game Breaking: Some players illegally set monsters from their hands into their Spell & Trap Card Zones just to have their hand empty...especially crude in that Konami refused to implement any kind of rules permitting players to be forced to show their set cards after a game.
Swarm-heavy archetypes are all the rage as of late. Consider the Six Samurai. Their Synchro Monster, Legendary Six Samurai - Shi En, can negate 1 Spell or Trap per turn, has 2500 ATK, and can destroy another Samurai in place of itself. Back before it was hit, players would be facing Shi En, several strong monsters, and a heavy back row and hand on the first turn. The game was basically over unless you had some excellent monster effects (and, frequently, even if you did). People were forced to fill their Side Decks with silver bullets because getting around Shi En was the bar you had to pass to be "competitive".
Xyz Monsters are Summoned by combining 2 monsters of the same level (sticking them under the Xyz Monster). Cards "attached" to an Xyz Monster aren't "on the field". However, for a short time there was a ruling that monsters whose effects activated when they left the field worked anyways. This led to Tour Guide From the Underworld, a card that can recruit Sangan from the Deck for an Xyz Summon, skyrocketing in price. Players would go for a big Xyz Monster, detach Sangan for an effect, and grab all kinds of monsters at no cost.
Tour Guide From the Underworld in general, even without the ruling, is extremely powerful due to its ability to make Rank 3 monsters easily. The Rank 3 monsters available can return low-level banished monsters for reuse, protect themselves from destruction while punishing the opponent for trying, or just stomp on everything with 3000 ATK. It can even grab a Sangan from your deck for Sangan's effect if you don't bother to Xyz Summon.
The middle one of those three bears further explaining — Wind-Up Zenmaines is the name of the offender. It's not very powerful points-wise, but whenever it would be destroyed, it can drop a material instead. Then, at the end of the turn it was forced to drop a material, it picks a card on the field and blows it up. If your opponent failed to play around it properly (or you tricked them into touching it; the latter is almost insultingly easy to do), they'd probly lose their best monster on the field, and you'd still having a monster left. Recall that you only gave up one card from your hand (Tour Guide — the other monster came from the deck) to play Zenmaines. You may cackle evilly now.
Reborn Tengu. If it's on the field, then gets removed from the field, another Reborn Tengu from your deck takes its place. Think about what that means when you use it for a Synchro Summon. Now look at how many Synchro Monsters are on this page. Not to mention it can be reused with Pot of Avarice. You guessed it: Tengu Synchro dominated a format (in the TCG, since it doesn't exist in Japan).
It has since been restricted to 2 per deck, matching the limitation on Destiny HERO - Malicious from the Tele-DAD deck. When Malicious is is in the Graveyard, he can be removed from play to pull out another copy from your deck. Since he doesn't need to be on the field to do this, you still have access to your Normal Summon. He cannot be returned through Pot of Avarice and lacks the battle strength of Reborn Tengu, but increases Dark Armed Dragon's playability later in the game.
The Destiny HERO engine, which uses Malicious as a Tribute and later as Synchro fodder. It has a good draw engine with Destiny Draw and Disk Commander, and comes in DARK which has awesome Graveyard support. 2 format-defining Decks used this engine to fuel their combo: the aforementioned Tele-DAD, and Perfect Circle, which combines Disc Commander with Monarchs and Light and Darkness Dragon to make a "circle" of plays that gives continuous advantage. By reviving Disk Commander every time LADD dies, you draw two cards, and can use it as Tribute for Monarchs or another LADD.
But that was only one reason behind Disc Commander's banning: Premature Burial, a graveyard revival card that due to the wording, does not result in the destruction of the revived monster if it leaves the field instead of being revived. To further elaborate, any card that returns cards to the hand (i. e. Giant Trunade, the aforementioned Brionac, Dewloren, etc.) can lead to revival abuse with this card, more than compensating for the 800 LP more often than not. With Disc Commander, this led to multiple revive-draw loops.
Airblade Turbo, which abused Diamond Dude's ability to activate Spell cards from the Graveyard without cost, was another arguably more powerful Game Breaker deck based around the Destiny HEROes. Mercifully, it only lasted for one major tournament so it isn't as infamous.
Heck, bounce cards are universally game changing. They remove threats from the field while evading destruction-negating cards, in addition to letting you recycle your on-field cards. Giant Trunade and Brionac were banned for this reason, though other cards such as Penguin Soldier are balanced by being relatively slow.
Plants, to the point of being Tier-Induced Scrappy. The problem with Plants was, they were a relatively fast engine for Synchro Summoning without using up the Normal Summon, and really consistent at that. Add to that the fact that it could manipulate every level for Synchro Summoning. To take this Up to Eleven, this engine is so versatile that it could be put in any swarmy Deck and work. See Reborn Tengu? This is the same group of cards that made one of the best variants of Tengu.
As an example of Sequel Escalation, some decks can be not so good at first, but with the release of new cards, can suddenly become great, to the point of gamebreaking. Such an example is Debris Junk Doppel. At first, the idea of Debris Junk was solid, being able to Synchro for level 5 or field nuke each turn. However, the strategy was deemed too slow to work. Several years later, on top of a lot of cards (notably the Plants) being released, one card named Doppelwarrior, which greatly increased the Deck's speed, took the deck to the competitive level. Finally, T.G. Hyper Librarian (a Game Breaker in its own right) was released, allowing a draw for every Synchro Summon. The speed with which the Deck can Synchro for 5 and still have a follow-up proved consistent enough that Junk Doppel became the deck of the format.
The poster child is definitely Rescue Cat. When it came out, it was a decent tutor somewhat limited by the single turn duration of the monsters it retrieves from your deck, which can only be beasts of level 3 at the highest. Gladiator Beast gave it a shot in the arm. Then the Synchro era happened, and X-Saber Airbellum, a powerful level 3 beast tuner, was available from the start. Cue mass first turn synchros. The card ended up on the semi-limited list, advancing each successive year until it was forbidden.
You may have noticed that the Envoys at the top of the page were the first example of a Game Breaker in this game. Now look at how long this page is; all of the examples below the Envoys were released after them, not all of them banned. The game has a crapton of powerful cards running around. Konami has noticed this and is now taking the risk of unbanning one of the Envoys. While it has to be drawn to be used (unlike Synchros and Xyzs that are always ready in the Extra Deck), it is such a consistent game-winner that time will tell whether it remains free or is condemned to the Forbidden List again.
Wind-Ups. They have a Special Summoning combo that takes some luck to set up, but leaves the opponent with zero cards in hand. On the first turn. You'd better hope you open with Effect Veiler or Maxx "C".
Rescue Rabbit. It gives you two Level 4 or lower Normal Monsters with the same name and destroys them at the End Phase. It was supposed to give Normal Monsters, seldom used in competitive play, the chance to be used for quick Xyz Summons. Someone figured out that you could use it to grab 2 Level 4 Dinosaurs and Xyz Summon an Evolzar monster, which can either negate 1 Summon/Spell/Trap or two monster effects, meaning that each one usually needs 2 answers. As a result, Rescue Rabbit, which was designed to encourage creativity, led to a deluge of nigh-identical Dino Rabbit decks...
Inzektors, which turn the notion of costs backward by actually gaining cards when they blow stuff up. If Inzektor Hornet is equipped to an Inzektor, you can detach it to blow up a card. It's used with Inzektor Dragonfly, which equips itself with Hornet, and when Hornet pops something, it Special Summons Inzektor Centipede, which also equips itself with Hornet, and when Hornet pops something else, it adds an Inzektor card to your hand. They can also pull off absurd One-Turn Kills by shooting two cards that are equipped to Dragonfly at each other.
Thousand-Eyes Restrict. A level 1 Fusion monster with a nasty effect of locking all monsters into their current battle positions and preventing them from moving or attacking. It might have no attack or defense, but it has a second nasty effect that allows it to absorb enemy monsters and add their stats to its own (face-down monsters give it no stats). Normally, you'd need a specifically designed deck to bring this thing out, but thanks to certain other banned cards (Metamorphosis, Tsukuyomi, Magical Scientist, and Magician of Faith), one could make a deck without the fusion card to bring it out. It single-handedly created an entire format that was so slow that the creators hit the deck harder than any other deck has ever been hit with the banlist, banning EVERYTHING that made the deck even remotely usable.
Demise, King of Armageddon is a level 8 Ritual monster. By itself, it's an over-costed Judgement Dragon with less attack. However, with the release of Doom Dozer and Advanced Ritual Art, this card became very broken. To elaborate, you would use Advanced Ritual Art to send two normal level 4 Insects to the graveyard, summon Demise, and pay 2000 life points to destroy all other cards on the field. Then you would remove those insects to special summon Doom Dozer (which has 2800 attack). Finally, you would use Metamorphosis to tribute Demise and turn it into Cyber Twin Dragon, which also has 2800 attack, but can attack twice. Three 2800 attacks is higher than 8000, so, good game.
Chaos Dragons. Perhaps hoping to hearken back to the days when Blue-Eyes was the biggest fish in the pond, Lightpulsar Dragon was made - it is easily special summoned from the hand OR graveyard, by either removing one LIGHT and one DARK from the grave or ditching one of each from your hand respectively. That would be only fairly good on it's own; what makes it brilliant (for you) is the fact that it yanks back a high-level DARK Dragon from your graveyard whenever it goes there, for no extra cost or disadvantage. Kill it, and something BIGGER takes it's place.
But still only brilliant. No, what earns Lightpulsar's place on this page is the fact that the prime candidate for his resurrection is one Red-Eyes Darkness Metal Dragon (REDMD). Not only is this guy huger than most commonly-played monsters, but he can be special summon himself very easily, and — and this is the important part — once per turn, he can summon any Dragon from your hand or graveyard for free. Like, say, Lightpulsar.
Bottom line? Once your opponent has Lightpulsar on the field and REDMD in the graveyard, resign yourself to dropping two cards' worth of destruction (at least) to getting the bugger off the field — and they can start it all over again next turn by discarding a Light and Dark for Lightpulsar. Cards which are run in large quantities in Chaos Dragon decks, for that same purpose.
Not helping is the fact that Dragons have the best specific-mill method out there; Future Fusion (which fuses from the deck to the graveyard) played with Five-Headed Dragon. They get to pick five dragons and dump them, no questions asked. If this isn't turn one and they've got a Chaos monster in the hand to start the banishing party (and start searching REDMD with another dragon's effect), you're thoroughly screwed.
Not only that, because of FHD's non-specific fusion costs (any 5 dragons), combining Future Fusion with Dragon's Mirror allows a second FHD to be summoned. This is a HUGE help if your Chaos strategy somehow goes amiss. Since FHD also can't be destroyed except by LIGHT attribute monsters, throwing in a DNA Transplant to make all monsters anything else can seriously ruin someone's day.
Fear not, loyal citizens, for the Heroes of Jaden Yuki are here! ...With some more broken tactics. Let's count them off:
Firstly, Neos Alius. Probably one of the most-supported cards in the game, period. The way you played him was you tributed him for Gemini Spark to blow something up and draw at the same time, then used Hero Blast to yank him back to the field and kill a low-powered monster into the bargain. That's already a two-for-three cycle. Now remember that Spark and Blast can be played pretty much anytime, meaning they can be chained to your opponent's destructive cards that would kill your own. Cunning play could see you bump that ratio up to a two-for-five.
Heroes have ridiculous searching power. The best in the game, arguably. Proof? Well, a 'modern' Bubble-Beat deck plays only seven monsters out of forty cards total. Despite that, it's practically guaranteed for a Hero player to end up with a monster on the field at the end of turn one.
Tying into the above, Elemental Hero Stratos. When he's Normal or Special Summoned, you could either search any other Hero or kill spell/traps equal to the other number of Heroes you had. He's a free tutor, on a powerful monster. It ended up banned in the September 2013 for how easily it could be and was abused, both in the above-mentioned Destiny HERO engine and the below-mentioned Bubbleman engine among others.
Stratos really comes into his own when combined with Bubbleman. Bubbleman can be summoned for free from the hand while he's the only card there. Then you use him and Stratos for the Xyz Monster Blade Armor Ninja, who can detach one material to attack twice. Summon Stratos, grab a Bubbleman, set your hand, drop Bubbleman, Overlay, do 4400 damage.
Miracle Fusion, comboing with The Shining. To wit, Miracle fused cards from your graveyard and field to the banished zone. The Shining requires that you fuse a Hero with any LIGHT monster. Stratos is a Hero. Neos Alius is LIGHT. And not only does The Shining gain 300 attack for banished Hero — meaning that he was typically an eye-watering 3200 Attack — but when he dies, he puts any two banished Heroes back in your hand. Translation: the Hero player dropped a spell card to recover two Heroes from his/her grave in a few turns' time, while getting a massive monster out in the meantime.
Do not be fooled with those puny Heroes. The single most broken Hero monster ever released goes by the name of Elemental Hero Absolute Zero. Easily Summoned by fusing a Hero and a WATER monster (like Bubbleman, or other commonly run Heroes), it has a very good 2500 ATK and gets 500 ATK stronger for each other WATER monster on the field. Most importantly, if he leaves the field for ANY reason (destroyed by battle, destroyed by card effect, banished, returned to the hand, sent to the Graveyard, even used by YOURSELF for a Fusion Summon or the cost of a card), ALL monstera your opponent controls are immediately destroyed. Most monsters with such powerful effects require to be removed in a specific way, either destroyed by battle, by card effect, banished, etc... Utterly broken, and one of the power cards of the Hero archetype.
Combine Absolute Zero with the quick-play spell Mask Change and you can summon Masked Hero Acid. What's so good about this? Absolute Zero gets tributed for Mask Change, meaning he gets his effect to destroy all of your opponent's monsters. Then Acid hits the field and destroys all of their spells and traps and knocks 300 attack off of anything that somehow survived Absolute Zero's effect. What's more, since Mask Change is a quick-play spell, you can pull this trick off during your opponent's turn.
Plus, they also have the advantage of Super Polymerization. Discard a card, get rid of one monster your opponent controls, and use it as a material for your fusion. There are 6 elemental E-Hero fusions, each of which uses 1 E-Hero and 1 monster of its particular attribute as materials. So you can ALWAYS get something out. Opponent has something to negate it? Too bad they can't respond to it at all.
The introduction of a certain Xyz monster has made an extremely powerful Otk possible, one that only requires you to draw only two cards: Fusion Gate and Chain Material. Chain Material lets you use monsters from your deck for fusion summons. Fusion Gate is basically a permanent polymerization, if at the cost of banishing the fusion materials. Ok, but when Elemental Hero Electrum is summoned, he shuffles any banished monsters back into the deck, so basically you're summoning him for free. Summon two of these level 10 fusion monsters and you can Xyz summon Superdreadnought Rail Cannon Gustav Max, who can detach one material to inflict 2000 points of damage on your opponent. Then fuse Gustav with the Electrum in your grave to summon Elemental Hero Gaia, which dumps the second Electrum that Gustav was using as an Xyz into the grave. Fuse Gaia with the Electrum in the grave to create another Gaia and summon a third Electrum with materials from your deck, which incidentally puts those other two Electrums (which had been banished) and Gustav back into your extra deck. Lather, rinse, repeat three more times and you win.
Many stun/lock cards, particularly Time Seal (used as a Yata replacement for awhile in a loop with Tsukuyomi and Mask of Darkness) and Cold Wave, which prohibits both players from activating or setting spells or traps, allowing the user to go straight for the kill, barring any monster effect use.
Makyura the Destructor and Temple of the Kings, both of which have effects that allow the controller to activate traps without having to leave them set for an entire turn. Temple of the Kings makes it a continuous effect.
Temple of the Kings is even worse with Mystical Beast Serket. MBS alone is a powerful threat, removing from play all monsters it destroys by battle, and getting an extra 500 ATK for each time it destroys a monster that way, which is only made impratical due to the fact that Temple of the Kings must be activated so it can be on the field. Then there's Temple of the Kings' other effect when MBS is on the field. Sending both cards to the graveyard allows you to Special Summon a monster from your hand, Deck or Extra Deck, much like Cyber-Stein described above, only better, you can special summon Synchro monsters like, say Shooting Star Dragon or Red Nova Dragon, or any of the Game Breaker cards described above that can be special summoned, without the 5000 life points cost. It's no surprise Temple of the Kings got banned (Mystical Beast Serket never got banned; it just cannot exist on the field without Temple of the Kings or Skill Drain).
Makyura is a candidate for the most broken card in existence as it has its own deck which can consistently win before your opponent can even get a turn off. While decks which constantly draw for their win condition (e.g. Exodia or Magical Explosion / Blasting The Ruins) are inconsistent and gimmicky in Advanced Format, Makyura immediately allows the additional use of trap cards with a drawing effect to easily thin out the deck. It also allows for the use of a first-turn Exchange of the Spirit, which swaps each player's Graveyard with the deck. On the first turn this means the opponent automatically loses for not being able to draw anything.
The Hieratic archetype hands down. A series of high level dragon monsters, most of them can be special summoned by reducing their attack. No big deal there. But when they're tributed alot of them can replace themselves with a monster from the deck, hand or grave, if at the cost of making that monster's attack and defense 0. No big deal, right? Enter Hieratic Dragon King of Atum, a level 6 Xyz monster that can summon any dragon monster from your deck. Including Red Eyed Darkness Metal Dragon, which can itself revive any dragon from the grave. Enter Hieratic Sun Dragon Overlord of Heliopolis, a rank 8 Xyz, which can destroy your opponent's cards by tributing monsters from your field or hand. Needless to say it takes some fancy footwork and a bit of luck to pull off a win against these guys.
The Dragon Ruler archetype is setting up to be this. A series of level 7 dragon type monsters with a set of smaller level 3/4 versions of themselves that can special summon them from the deck. They have a plethora of effects that can enable swarming and rapid summoning of rank 7 Xyzs, along with a means of getting Light and Darkness dragon onto the field on the first turn. Sure, you can only use one of their effects per turn and even then only once per turn, but the sheer speed and consistency of these effects more than makes up for it with consistency, power, and other effects and the smaller dragons are instrumental in overriding this limitation. And it's for this reason that this deck is so widely hated before it even came to the TCG.
How powerful was the Dragon Ruler deck? Duelists have demonstrated that with the mini-dragons, it could even beat TeleDAD in it's prime! The only thing that kept it from being Tier 0 was the other Game Breaker mentioned below.
More to the point: After a format of dominating the game, they were struck hard by the banhammer, losing much of what gave them such exceptional speed and power, including the complete loss of the smaller dragons...and now, in the following format, they are still the top deck in the game.
Prophecies had their own gamebreaker in the form of Spellbook of Judgement. How it works is that for every spell card that you activate after you play it, you get to search for a spellbook spell card at the end of the turn AND special summon a spellcaster-type monster whose level is less than or equal to the number of spellbooks you added to your hand. A popular target for this is a monster called Justice of Prophecy, a level 3 monster who can be banished at the end of the turn to add a high level spellcaster, like the deck's ace monster High Priestess of Prophecy, and another spellbook, like another Spellbook of Judgement, to the hand. Essentially, all one has to do is play Spellbook of Judgement and three other spell cards (not a hard task to do in this deck), and they have their ace monster and a whole hand of support spells ready for the next turn.
Spellbook of Judgment has actually been banned because of this.
And, last but not least, any and all cards that currently occupy the Forbidden List. By that list's very nature, any card that winds up there is too broken for its own good, and would heavily skew the game in a player's favour if they're used in any number. There have been cards that have been banned since the Forbidden List was first drafted, and they still haven't left after close to a decade. Edo (a once popular webhost who ran one of the most popular Yu-Gi-Oh TCG websites), had this to say about it in his 2005 "Copaca-BAN-a!" article, and it still applies to this day:
Edo: As a prophecy, I can tell you that you should never expect Raigeki, Harpie's Feather Duster or Yata-Garasu to ever leave that list.
Cyber Jar was an extremely powerful staple in many decks before becoming banned. When flipped, it nukes the entire field and forces both players to reveal the top 5 cards from their deck and Special Summon all Level 4 or lower monsters in face-up attack or face-down defense, with anything else being added to the hand. It served as a "get-out-of-jail-free" card, usable in any bad situation, that also gave the user a significant field and hand advantage.
Cyber Jar had an entire deck built around a first turn kill using cards like The Shallow Grave, Book of Taiyou, and Card Destruction to deck the opponent out before they can draw. Americans tried fixing it by restricting Book of Taiyou which worked, but since the World Championship didn't have such a restriction, it dominated the tournament leading to Cyber Jar's death.
Its cousin, Fiber Jar, was even worse. Got a bad hand? Close to losing? One of your Exodia pieces accidentally went into the Graveyard? Fear not! Just flip up Fiber Jar and it sends every card on both players' fields and their hands and Graveyards back into the deck while drawing 5 new cards, effectively resetting the game.
In the early days, simple mistakes in card effects made certain cards far more powerful than they should be. The Labyrinth of Nightmare set featured cards that banished monsters from the graveyard to activate effects, but before their errata came out, the text implied that any type of card could be used. This made it far too easy to fuel Bazoo the Soul Eater and Skull Lair. Even worse was Infernalqueen Archfiend. Before the errata, her ATK boost each turn was permanent, meaning she could become even more powerful than Blue-Eyes in only a few turns.