Old time wargamers of the Avalon Hill type may remember the nightmarish nonsense—like losing all of the British Empire to an attack carried out on London by a single airborne unit—that followed trying to play Rise and Decline of the Third Reich in its first edition in the mid 1970s. (The game's designer, John Prados, is brilliant at concept but, even in the seventh edition published in 2000, proved that he STILL can't write rules for doodly.....)
Apparently, the official rules of chess once had a loophole that rendered the game 1.e4 e5 2.Bc4 Nc6 3.Qxf7 mate a victory for White. Although the White Queen cannot move this way legally, checkmate ended the game. The other side could only claim an illegal move while the game was in play. After a checkmate, legal move or not, it was too late. This is just the most famous example of how this major flaw in the rules could be exploited.
The current FIDE Laws now state that checkmate ends the game, provided the move that brought it about was legal. Which ends that one.
For a while, there was no rule that you couldn't promote a pawn into an enemy piece to block the other player's path.
There is a similar case of promoting a pawn into a king. (Some stories have this "loophole" as a misunderstanding of the rules by a newcomer, caused by an incomplete explanation by his opponent, and the newcomer insisting on following the rules as first explained.) Although technically, this makes it worse for the player, as the rule is that someone whose king has been checkmated has lost the game, so having two kings is just two ways to lose. (Although if you were very clever, you could combine this with the previous loophole and promote a pawn into an enemy king. Bonus points if it's in a position already in checkmate.)
Castling can be performed with a king and a rook which have never moved from the position they were placed. Which led to someone promoting their king's pawn into a rook and using it to castle vertically, until the rules were rewritten to prevent this.
Scrabble. It is, technically, perfectly legal to play words that don't exist - you just have to pay the penalty if you're challenged. If you can bluff your opponents into thinking it's a real word and not challenging, you're good to go.
There's a reason the comprehensive rules and errata for Magic: The Gathering is hundreds of pages long and reads like a federal tax code. The rule-makers are constantly having to close odd loopholes the players figure out with each new batch of cards and the thousands of possible interactions that open up.
The other loophole was for the opposing player to catch the card in the air then either hold on to it (thus it never landed), or drop it on any card they choose. Errata for the eventually specified that you couldn't interfere.
If there was such a ruling (they weren't systematically recorded in those days), it was overturned in 1994 with a Word of Godruling that tearing up the card made it "marked" and you would lose the match for playing with a marked card. You would then be required to replace it with another Chaos Orb before the next round started or you would lose that match for illegally changing your deck configuration. Loophole Abuse cuts both ways.
This was subsequently parodied in Magic: Unglued with the card "Chaos Confetti".
When used as intended, Chaos Orb spawned another loophole: players would spread their cards out over a ludicrously large area so Chaos Orb couldn't touch more than one when it landed, or would lean their cards against things so that it was impossible to land on top of them at all. A ruling has since been made that you can't rearrange your cards after Chaos Orb enters the game; also you must not have your cards stacked or in places where your opponent can't read their name or count them.
An urban legend claims that in one tournament, a player cast a spell with the effect "Target players loses the game," then pointed at a completely different table and said "That guy." You can't do that, even if nothing in the rules state the target must be in the game you're playing. That's not something necessary to state explicitly. You can't cast a Lightning Bolt at a player in another game either, or cast Control Magic on one of his creatures, or Counterspell one of his spells.
And just like with the Chaos Confetti, Wizards of the Coast make fun of such urban legends with their "un-sets". In Unhinged there is a card that specifically lets you destroy any silver-bordered card (only the un-cards have silver borders, regular cards have either white or black borders) in any game that you can see from your seat. Some players have used this to destroy cards from completely different card games because they are still, technically, legal targets as long as they have silver borders.
The cards of the Wish cycle specify "You may choose a card you own from outside the game and put it into your hand." This doesn't require it be a Magic card, so what's to stop you from grabbing an UNO Skip card, or Prof. Oak's New Theory? If you don't want to be that ludicrous, why not pull joke cards into serious games? (Errata for tournament purposes limit legal targets to cards in your sideboard, but for casual play, everything is legal)
Actually the rules of the game take care of this situation. From the rules:
When a rule or text on a card refers to a “card,” it means only a Magic card.
The card Mindslaver had to have an entire rulebook printed for its original incarnation due to players using it to do things like forcing their opponent to concede the game. In the some two dozen sets that have come since then, only one other card will ever use those rules (being the original Sorin Markov's ability).
Passing an item hand to hand is a free action (doesn't take up time), so if you line up a few thousand people you can get an object to travel miles in six seconds. Then the last person throws it. This is commonly called the "Peasant Railgun". note The end result is a regular thrown object, since Dungeons and Dragons only bases thrown-object damage on the strength of the thrower and size of the object.
You can also have one player stand on another player's shoulders and pick him up as a free action. Then the other player picks him up. Since this is all a free action, there is no time for them to fall, and thus they can fly by repeatedly picking each other up in midair.
If you have someone in a grapple, you can move them at a fraction of your normal movement speed, assuming they fail (or don't try) to resist. So if you have a half dozen people or so in a group hug and none of them resisting, they can travel faster than running speed. Get enough people and you can break the sound barrier.
Further, all characters in a grapple are in the same square. There's also a rule that up to three people can grapple with one target. With some creative planning on the part of the grapplers, you can get it so that the entire population of a planet is in one square, which is 5 feet in game terms. There's also a rule as to what happens when players break a grapple (each member of the grapple is shoved to the nearest empty square immediately). This can result in characters going faster than the speed of light in order to land on a properly empty square.
Dropping an item is a free action, as well. And if you happen to be fireproof and are standing next to an enemy while carrying, say, five hundred units of alchemist's fire... Though the logistics of actually carrying all of it is a bit screwy in and of itself (seriously, you normally only have two hands with which to drop them).
Perhaps the most true-to-form example of this trope (at least by the alternate name, Ain't No Rule) is that while the state of "Dying" is explicitly defined in the rules as far as what actions are acceptable, the state of "Dead" has no restrictions. There Ain't No Rule preventing a freshly-killed player from standing up and continuing the fight.
There's no official restriction preventing you from using the spell True Creation to make planet-destroying quantities of antimatter.
The various settings tend to have in-universe cases somewhere in all the history and organizations. For instance, House Jorasco healers are not supposed to treat without payment in money... but there is nothing hindering them from lending the necessary money and then setting a task as repayment in kind for the loan.
In universe, the infamous Wish spell. This spell can be cast by high level wizards, or can be granted by a few select creatures (like djinn), but they should always be met with caution. It is explicitly stated in the rules that wishing for anything too powerful can result in a perverted or partial wish fulfillment. Too careless wishing can result in getting the exact opposite of what was intended, depending on the maliciousness of the creature and/or the DM. For example, when wishing for a mighty artifact, the caster might grant you the artifact... by teleporting you into the tomb where the artifact is located, in the middle of its undead guardians.
In the universe (or multiverse) there's also the case of the Deal with the Devil (more or less literally). These vary, but may involve a Magically Binding Contract that the fiend itself also has to follow, but which will definitely be written with loopholes to turn against the mortal party — at least as much so as the fiend can make it, and they'll typically have centuries of experience. Both the Lawful Evil devils and the Chaotic Evil demons do this. (However, in an interesting interpretation, some guy who thinks about this stuff a lot claimed that Lawful Evil creatures will follow the spirit of the contract, not just the letter, since twisting the wording would be Chaotic. This is still presumably meant to allow a higher-level Loophole Abuse. However, this is not the way it's usually seen.)
"That's not the purpose of [Go Up A Level cards], but it's so vile and Munchkinly that we love it too much to say no." Steve Jackson Games, on whether Go Up A Level cards could be used on enemies to provoke monsters that ignore characters below a certain level.
People holding as many cards as possible in your hand and doing whatever they can to prevent others from noticing that they're holding more than five are cheating. Contrary to what some urban legend claims, it's not legal to cheat in Munchkin.
Early versions of the Loaded Dice card did not specify that the value you choose to replace that of a die roll had to be between one and six. And there are plenty of cards to abuse this with, like one monster that gets a bonus to its level equal to the roll of one die.
Munchkin is made for this. Literally. The rules are full of ambiguities, because it's supposed to recreate the experience of playing with (and as) a rules-lawyering, loophole-abusing dyed-in-the-wool munchkin. It may not be legal to cheat, but you're encouraged to take advantage of every ambiguity possible and if you can convince the others (or at least the owner of the copy being played) then you're free. The "legal to cheat" legend comes from another Steve Jackson Games card game, Illuminati, where it really is Not Cheating Unless You Get Caught, because why the hell would ancient conspiracies play by the rules if they didn't have to? (A munchkin's true power comes from abuse of the rules, not just ignoring them, after all.)
The Lore of Blood Bowl is rife with coaches doing whatever it takes to win. For example, players are strictly forbidden from carrying weapons on the pitch. Where most players figured it didn't count as a weapon if the blades were fixed to the armour, the Dwarves argued it meant riding a bulldozer on the field was allowed - it's not carried, is it? The actual gameplay reflects that spirit. In first and second edition of the game, the rulebooks for the various ways a player could cheat were almost as long as the actual game's rules (and more byzantine).
The concept of Pledges from Changeling: The Lost practically begs the player to use this trope; as is frequently the case with The Fair Folk, neither the True Fae nor Changeling Pledges recognize any such thing as "the spirit of the agreement." You just have to make very, very sure that you actually know what you're doing.
An in-universe example from Warhammer 40,000: following the Age of Apostasy, the new Ecclesiarch Sebastian Thor declared the Decree Passive, in which the Ecclesiarchy was forbidden to maintain men under arms. Thor's predecessor's Bodyguard Babes, the Brides of the Emperor, were allowed to continue operating as the Adepta Sororitas because Thor knew the Ecclesiarchy needed a militant arm and internal regulation; they were not "men" under arms, even though it violated the spirit of the decree.
The FAQ articles have had to correct some in the past. The Swooping Hawks's Intercept rule reads "the unit never requires worse than a 4+ to hit an enemy vehicle," which means, for instance, that the WS 4 Swooping Hawks could hit a WS 5 Venerable Dreadnaught on a 4+ instead of a 5+ as the normal Weapon Skill table would indicate. An Ork list that was designed entirely around exploiting the wound allocation rules in fifth edition by giving every model in every unit different gear was briefly popular on the tournament scene.
Units may fire out of the windows of a building. The rules don't prevent units with "barrage" type weapons, like mortars, from firing "through" the roof or windows of the building their operators are in.
This trope is Mr. Welch's bread and butter, even if the GM doesn't tend to be cooperative. The phrase "even if the rules allow it" and variants thereof appear no less than 47 times throughout the ever-growing list.
There are a lot of infamous combinations which resulted in continuous loops in Yu-Gi-Oh! that result from this. The vast majority of them involves exploitation of the ruling that, except in very rare cases, a monster's effect is "reset" when it is flipped face-down or removed from the field temporarily, allowing you to reuse the same effect multiple times in one turn, with the right setup. There were even entire decks constructed around this.
Before it was banned, the card Last Turn was the subject of quite a few loopholes, mainly because it didn't negate monster effects while it was in use. To wit, when it's activated, both players choose a monster to be on the field (the activator from their field, the opponent from their deck) and battle; whoever has a monster remaining on the field after the battle wins, otherwise it's a tie. Thing is, the monster left on the field doesn't have to be the one the player chose for the battle, and the card doesn't negate monster effects, so if you have a monster on the field that can prevent Special Summons (thus, preventing the opponent from getting out their chosen monster), or one that can summon out a monster when destroyed (thus leaving you with a monster after the battle), you can easily screw over the opponent with it.
Lava Golem is a card that requires you to tribute two of your opponent's monsters to summon it to your opponent's field. Because Lava Golem's effect is technically a cost to play it, rather than an effect, and because it technically doesn't destroy the tributed cards, it's attained a level of fame as one of the only monsters that can kill literally anything, regardless of circumstance.
in the Axis And Allies miniatures game, air units were a late addition, meaning a lot of previous cards weren't prepared for their entry. Thus, units that should not be able to attack planes, like mortars and certain assault guns, can. Worst of all, land mines can affect planes. Those are some epicallybouncing betties.
Errata dictates that units with the "bombardment" ability can no longer attack planes, eliminating most ground artillery from the equation, but mines and mortars are still okay.
A robot-class player or NPC in Mutant UA could have drones as an "option." Maximum would be 4 without any penalties for too many options, but drones could have their own options, deliberately so for the sake of being useful, but nothing states they couldn't have drones as well. Cue infinite horde of massively powerful drones! (although rule 0 almost always stops this as it's crazy-powerful).
In the CCG "EVE: The Second Genesis" one of the main ways to gain money (used to play further cards) are location cards. One such location has the effect "When this card comes into play, sacrifice a location". The officially sanctioned loophole around this is to play the card into an uncontrolled region. Because the region is uncontrolled, the location is uncontrolled too and the effect does not activate...
Illuminati had a particularly legendary example during its first tournament. The final match dragged on for a long time, until one of the players offered half the prize money if his opponent would forfeit just to end the stalemate. They shook on the deal...and then the first player used the card "I Lied◊". The judges ruled that the move was well within the spirit of the game and, over his opponent's voiciferous protests, declared him the winner.