The Baldur's Gate series has featured many game breakers throughout its various installments.
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The "talk-fight" bug made it possible to attack an NPC who normally talks to you, talk to them when they turn red, and repeat the process until they died without landing a hit on your party. This could be done with most creatures in the series, including bosses and dragons.
Baldur's Gate II
The various "kill undead instantly unless they save" weapons, which allow you to instantly kill any undead boss in a single round, since there is no effective defense against it whatsoever and you could easily get up to 8-10 attacks per combat round even in medium levels. It even turns nasty Bonus Boss Kangaxx, considered the strongest opponent in Shadows of Amn, into an Anticlimax Boss. Despite the fact that, normally, the Mace of Disruption wouldn't be able to harm him, as it maxes as a +2 weapon (Though as per it's Pn P incarnation, it can hit as if +5); demi-liches can't normally be hurt by anything less than a +4 weapon, of which there's only a very small number in Shadows of Amn (a dagger, two halberds, two staves, and two two-handed swords, one only Paladins can wield and the other only Evil characters can wield).
The Staff Of The Magi. Upon equipping it, it makes the character using it go invisible. You can walk up to someone, hit them (thus breaking your invisibility), and then immediately go into your inventory and just by clicking on the staff, re-equip it, including reactivating the invisibility. Rinse and repeat, and very very few enemies can do a thing about it.
Several minibosses/dragons were vulnerable to the instant kill spell Finger of Death, such as the Shadow Dragon - A creature that the game assumes most lower level characters would want to quietly sneak past. Most bosses /minibosses in the game were immune to instant kill though.
The Drow armor and weapons that are found in the Underdark (including the Drow Full Plate +5, the best suit of armor in the game) cannot normally be removed from said area without disintegrating into dust as soon as sunlight touches it. That is, unless (when you're in the Underdark) you give all the equipment you want to keep to one of your party members, reform your group and remove said character, and ask him/her to meet you at the Copper Coronet. You can rendezvous with them as soon as you exit and get all of the armor back, making things significantly easier for the rest of the game.
Traps, in all their forms:
The traps of epic level Thieves, which are so nasty strong they can, among other things, instakill the Throne of BhaalBonus Boss Demogorgon after you've installed a mod to specifically make him much tougher. Specifically, an unintended effect is being able to lace traps beforehand at the location where Demogorgon — or Irenicus in Suldenessellar, for that matter — will spawn when attacking, instantly scoring as many automatic hits as you like. You can send any enemy careening into a series of traps by leading them there with a Ring of the Ram.
Bards could also get epic-level traps... and, since they had no "set traps" skill, they succeeded automatically. This for traps that could freeze time.
If you play a bounty hunter, you get special traps that not only did more damage, but could be thrown. Since traps had a pretty big area of effect, this meant that the thief could throw a trap, hide, throw another, hide again, etc. Even more absurd, you only had to do this once at level 21+ because these traps mazed enemies, which meant you could now send in the rest of your party to slaughter them one by one as they popped out of the maze one at a time. Then there were spells like Death Fog, which did damage over time and had such ridiculous areas of effect that you could engulf enemies from outside their visual range.
The seller inside the Shadow Thieves' base will buy stolen objects (unlike any other shop in the game). This means that, for a Thief with a high pick-pocketing skill, you could sell-steal-sell again-steal again-and so on some expensive object and become ludicrously rich in a heartbeat.
Several absurdly-broken spells destroyed any notion of difficulty in the game:
The combination of the Robe of Vecna and Amulet of Power (lower casting time) with the high-level spell "Improved Alacrity" (cast spells immediately one after the other, instead of a one spell per round limit), which allows a mage to pull off the magical version of Beam Spam. You could combine it with Time Stop (everything except the caster freezes in place for six rounds) to have your enormous Spell Spam assault hit the enemy with dozens of spells before he can do anything. If your enemies are still alive after that, just cast Wish to replenish your spells and do the entire thing over again. To increase effectiveness, you could turn on autopause and set it to "when casting ends". This way you will maximize number of castings during Improved Alacrity. Alternately, you could cast Simulacrum beforehand, which lets you do all of the aforementioned twice.
This combination is even more effective (if that's even possible) when you're a high-level sorcerer, when you can easily cast 9 of the most effective attack spells of every level, instead of only those of you memorised spells were atttack spells.
Projected Image, a spell that created an illusory copy of the caster, including all of his spells. Meaning that the Image could do everything already mentioned above, whilst leaving the actual wizard in complete safety. If, by some miracle, the Image was killed, then the wizard could just cast it again. Projected Image is also capable of doing some things your regular mage can't. For example, there's an "epic level" spell that lets you summon a planetar, a powerful fighter/mage/cleric hybrid that can contend with most monsters in the game. Downside? You're limited to one, but the projected image can make as many as six.
Another great thing about Simulacrum and Projected Image is that they copy the items in your quick slots as well. Buy some powerful scrolls, put those scrolls in your quickslots, create a copy of yourself, and let them use those spell scrolls without using up the original scrolls.
Cloudkill and similar Area of Effect-spells. You can often cast them close to powerful creatures or a group of them, as they won't see you and probably won't move a spot. They also stacks.
You can easly kill Firkraag the Dragon with this trick.
Before Cloak of Reflection was nerfed by the developers, it reflected all spell damage back onto the caster - which meant that if you protected yourself against nasty non-damage spells, you could get Irenicus to kill himself with Cone of Cold in the first part of the final battle (before you go down to hell). Even after the nerf, it made you immune to spell damage (it just didn't reflect it). You could, fairly easily, make yourself completely immune to damage or any negative effect whatsoever (especially as a fighter/mage).
In a game full of potentially-overpowered companions, Keldorn stands alone. You can immediately acquire him in Chapter 2 by accepting a mission in the Temple District and finding him in the Athkatla sewers. He comes equipped with a unique set of Full Plate Mail +1 armor (with several bonuses, including Free Action), the best Paladin kit in the game, the Dispel Magic and True Sight abilities (which makes magic-wielding enemy encounters a breeze) and, once you get him Carsomyr from Firkraag's dungeon and the Gauntlets of Dexterity, he becomes a juggernaut. It says something when, in a game where most bosses' HP top out at just over 200, Keldorn with Carsomyr can dole out 30-35 damage per successful swing. He can solo Irenicus in his second form via spamming True Sight, and he even makes Insanity playthroughs insultingly easy.
Even 'worse', the Dispel Magic innate ability his class kit gets has special rules which allow it to be cast instantly (speed factor 1), and at DOUBLE his class level. This makes it almost the most broken spell in the entire game, as it means Keldorn can dispel any level-appropriate mage encounter with a nearly 100% success rate, then slaughter him inside two rounds. His True Sight innate ability also makes a lot of enemies which rely on abusing Improved Invisibility (cannot be targeted by spells) trivially easy to lock down and obliterate.
Assassin's poisons if you use them in ways the developers probably didn't intend for you to.
Is your character a mage? With even halfway decent stats? Then you've got dozens of ways to break the game.
Cloudkill and similar Area of Effect spells. You can cast them near enemies and run away. If they don't see you through the Fog of War, they will likely just stand there and die. You can easily kill Firkraag the dragon with this trick.
The Animate Dead spell once its caster reaches level 15. The large skeleton summoned at this level is very powerful, has a ton of hit points and is immune to almost any sort of magic cast at it. Additionally, it will willingly auto-navigate through fog of war to seek out and kill enemies you can't see and can take out packs of beholders on its own without putting your own neck out.
Inexperienced players sometimes underrate Aerie as a mage because she doesn't gain access to the most powerful arcane spells, but the ability to use divine as well as arcane spells with power-amplifying setups like Sequencers and Contingencies more than makes up for it if you know what you're doing. Although, being a multi-class, she won't actually level up enough to get Sequencers until very late in the game.
More horrifyingly (in a good way), being a mage gives her access to the robe of Vecna, which decreases ''all' casting times. Including her cleric spells. Stack on the Amulet of Power and Heal spells become a viable method of in-combat instant healing.
The combination of the 9th level spell Chain Contingency and three Abi Dhalzim's Horrid Wiltings, set to cast at the nearest enemy on sight. This is capable of doing 250 damage to the target, which will easily kill any non-boss enemy, and works horrifyingly well against some of the most powerful bosses in the game, including Draconis and Demogorgon.
A high enough Turn Undead ability can kill nearly every undead, even vampires.
It's only possible if you're playing the second game or the Updated Re Release, but: human dual-classed Kensai/Mage. All of the hitpoints and combat prowess of the Fighter, the Mage's ability to cast devastating arcane spells (as mentioned above), with the added abilities of higher THAC0, damage and attack speed in melee, as well as the ability to use a "Kai" that causes hits to deal maximum damage while it lasts. All this at the cost of giving up armor, which a Fighter/Mage can't use anyway until they find the rare Elven Chainmails at the end of Shadows of Amn.
The Kensai/Mage is almost the exact definition of Magikarp Power if you try to take it through the entire trilogy. In the first game, your AC is horrible and the lack of proper ranged weapons (unless you specialise in axes or daggers) crippling. In the second game, depending on when you decide to dual-class, you either have to go through most of the quests in chapter 2 or spend the entire spellhold-underdark-chapter 6 sequence as a sub-par mage catching up to the rest of your part. Once you hit Throne of Bhaal, however, you are a terror. (At which point some would argue multiclass fighter/mages probably out-gish you anyway since they get fighter High Level Abilities and dual-classes don't).
The Berserker/Mage has almost all the advantages of the kensai/mage, but trades lower melee damage output and accuracy for a berserker mode that No Sells almost every Standard Status Effect in the game, including mazing and imprisonment, and the ability to wear armour and bracers. Furthermore, berserkers are much less of a Glass Cannon than a Kensai and are much more worthwhile in Baldur's Gate 1.
Similar to the Kensai/Mage example above is the Wild Mage, normally only available in Throne of Bhaal, but which can be modded to be playable in the first game. The class exemplifiesMagikarp Power, especially through use of a glitch where piling Chaos Shields in a Minor Sequenecer, and later a Spell Sequencer, led to the shield bonus stacking. The result was about an 80% defense from wild surges, meaning you could use Nahal's Reckless Dweomer with impunity. For those who don't know, Nahal's Reckless Dweomer is basically a spell that lets you cast any spell in your spellbook. It doesn't matter if you don't have it memorized or if you aren't high level enough to cast it—with that Dweomer, you can start flinging around Disintegrates and Horrid Wiltings as low as level nine. That's not the end of it, though—the spell Limited Wish, with high enough Wisdom, allows you to restore all low level spells. Nahal's Reckless Dweomer is one of those spells. Since Limited Wish can also be used to restore your health, this effectively eliminates the need for the Wild Mage to rest—s/he can just keep fighting for the entire game without once going to sleep, cycling through Nahal's Reckless Dweomers and Limited Wishes to restore health and spells as needed.