Infinity+1 Element

Elemental Rock-Paper-Scissors is an extremely common tactic for video games, and even outside of the RPG genre where it originated, it's one of the more common RPG Elements. Whether it makes use of Fire, Ice, Lightning or The Four Elements, or even some unique proprietary system, it's fairly common for games to make use of some "circle" of elements. Depending on the number of elements in the system, one element is weak to and strong against one other element specifically, or there are several distinct weaknesses and strengths for every set.

Sometimes.

However, Bosses (especially bonus ones) and Olympus Mons don't always play by these rules. So frequently in RPGs or games with RPG Elements, you'll encounter a rare Mon, spell, or other doohicky that doesn't play by the rule of Elemental Rock-Paper-Scissors. It frequently has its own unique "element," shared by no (or very few other) monsters, spells, weapons, or whatever. It belongs to an Infinity+1 Element. Said element generally has the following traits:


 * In Elemental Rock-Paper-Scissors, is resistant to (or is at least not weak to) every other element.
 * Sometimes, its only weakness will be itself.
 * In the same system, is frequently strong against every other element.
 * Belongs to a very small subset of the population of spells, Mons, or weapons; usually 5 or fewer.
 * Is hard as sin to get, and usually unavailable until near the end of the game. If it is available at all.
 * Has a "special" symbol or color which breaks the theme of the other elements.

Naturally, the ability to be strong against every single element makes these types of things more or less an intentional Game Breaker, so they're generally hidden at the end of Bonus Bosses or That One Sidequest. Sometimes overlaps with Non-Elemental, though Non-Elemental monsters tend more toward being Jacks of All Stats --Infinity Plus One Elementals tend to be better at everything. Sometimes takes the form of an Eleventh-Hour Superpower. Compare Element Number Five, which may overlap.

Tabletop Games

 * Dungeons and Dragons tends to do this with certain spells.
 * There are very few enemies who can resist sonic damage, and many are vulnerable. Wizard/Sorcerer sonic spells deal less damage than fire/cold/lightning counterparts.
 * Sonic and acid damage in Edition 3.5 were so useful as a means of bypassing damage resistance that the Archmage class' ability to swap elemental types about was considered very powerful even when it cost them one of their most powerful spells.
 * Force. Magic Missile is a Boring but Practical staple spell that deals force damage. Forcecage and Wall of Force are basically unbreakable barriers unless you carry a specific counterspell. Even better, Force spells deal with those pesky incorporeal creatures.
 * Damage from "divine power" is explicitly not resistable by anything. Unfortunately there is almost no means of dealing it except feats that convert only half of a spell's damage to divine. As this results in a net gain of zero damage unless the target's energy resistance would have soaked over 50% of the spell's base damage, or the caster is using a spell the creature is 50% resistant or immune to, it's mostly Schmuck Bait.
 * A handfull of other spells such as Bebilith's Claw forget to actually specify what type of damage they deal, which should imply they have no type and as such are not resistable by anything. Force's ability to negate incorporeality is potentially still more useful, though.
 * In 4th edition, out of the nine types of elemental damage, Radiant and Psychic have the combination of not being resisted by many creatures and having excellent support in terms of items and feats (with Radiant also being Super Effective against just about all undead, who tend to have a decent presence in most campaigns). Thunder, Lightning, Frost and Fire are all well-supported with some powerful tricks even when resisted, while Acid is basically neutral. The only stinkers are Necrotic and Poison damage, since they have few unique tricks and are commonly resisted by many enemies (such as undead), with many creatures who are outright immune to poison entirely, necessitating the odd Obvious Rule Patch for those who wanted to poison their foes.
 * Universal spells/creatures/relics in Magi Nation. All Magi can use them without extra cost, all Magi can use Universal relics, and they tend to be pretty powerful, too. As you can imagine, actual Universal Magi (who can use everything) are really, really rare--and all promotional, to boot.
 * Let's put it this way: the single most famous hero in the setting, Rajye, is Universal.
 * Biolith in Eye of Judgment.
 * Sunburst in Chaotix.
 * Void and Demon Chi in Weapons Of The Gods.

Video Games

 * Pokémon has had several throughout its existence. Dragon types were arguably supposed to be this for Generation I as it resists Fire, Grass, Water, and Electricity, so no matter which starter you picked you were at a disadvantage. Add to it, there was only one dragon type family and only the Final Boss used them. (Until at least the True Final Boss / The Rival was revealed.) Throughout the series a number of legendary and pseudo-legendary powerhouses are part-Dragon.
 * Psychic as well, thanks to monstrously huge Special stats characteristic to 'mons with the typing, powerful attacks, and lack of any real threat from opposing elements. Also from a story perspective the Bonus Boss Mewtwo and the uncatchable Mew were both Psychic types and like Dragons a large amount of legendary and pseudo-legendary Pokemon have been Psychics over the years. However with the introduction of the Dark typing, the Special Attack/Defense split, and better viability of already-existing super-effective elements in the second generation, it was thankfully taken down a few notches.
 * Steel-types also count, due to the fact that they resist ELEVEN out of the 17 types and are completely immune to Poison to boot. In fact, they are the only type that resists Dragon-typed attacks, and their resistance to Psychic also helped to contribute to Nerfing that typing in Gen II, along with the addition of the Dark type. That being said, Steel-typed attacks are not that great (due to hitting only two types super effectively compared to four that resist it), and moves with types that counter Steel-typing - Ground, Fire, and Fighting - are pretty easy to get a hold of. Earthquake in particular is downright ubiquitous in competitive play.
 * XD only - Shadow power is explicitly this on an offensive level. Shadow moves aren't very effective on Shadow Pokemon (the only Pokemon that can use Shadow moves), but super-effective against everything else! Due to Shadow Pokemon being exclusive to Cipher and its affiliates, not a soul outside of Orre is aware of this. Maybe it's better that way.
 * In the obscure Game Boy Color RPG Li'l Monster, the "Star" element is one of these--it breaks the card suit theme of the other "elements." Only one Mon, the Final Boss, is Star-type naturally, but it drops a gem that will turn your monster Star-typed, making it strong against all suits.
 * The Boss-types in Dragon Quest Monsters games--they're hard to breed, and resistant to most magic types. They also have fast-growing stats. But be warned! Getting even the first one (the basic Dragonlord) is a timesink and a half.
 * In Fossil Fighters, Olympus Mons Frigisaur and Ignosaur  have a special black "Legendary" element no other types have. They're resistant to most attack types. The sequel, Fossil Fighters Champions, introduces five new Legendary mons in the form of.
 * Eternal Darkness. Mantorok-aligned spells. The other three ancients had a clearly defined Elemental Rock-Paper-Scissors deal going on. Mantorok's rune was hidden in a secret area halfway through the game, and casting your spells with it had some very game-breaking effects, such as turning your character completely invisible.
 * According to the plot, the as-of-yet-unrevealed yellow ancient is this, as it can counter all four of the others.
 * The Almighty element in the Shin Megami Tensei series that can't be resisted, repelled, or negated. However, by the same token, nothing is weak to it, either. It's both this and Non-Elemental. Almighty spells also tend to be a horribly inefficient use of your MP, as elemental spells can be boosted through skills or accessories to deal more damage while using up fewer magic points.
 * Final Fantasy Crystal Chronicles example: The last element your Crystal Chalice can get is, and can be used to bypass miasma streams of any element.
 * Though it does come with the cost of not granting the bonus immunities that the base elements did.
 * The Disgaea series generally has 3 elements - Fire, Ice and Wind - with every enemy having varied weaknesses and resistances to each. And then there's the 'Star' Element, which nobody resists or are weak to. It's not quite the same as being a 'neutral' type, though, since there are enemies that will resist non-type damage (and quite well, at that), but nobody resists Star. Star-type spells are very useful against bosses in particular, since they tend to be resistant to all elements, and have high physical defense...
 * The Bulbmin in Pikmin 2 are resistant to all overworld hazards, instead of just the standard one the rest of the colored Pikmin are. The game Nerfs them, however, by making it so you can't take them out of the dungeon you find them in.
 * World of Warcraft has its magic attacks split to schools by damage type. There's fire, frost, nature, arcane and shadow. While no enemy is really weak against a particular school (barring some special cases, like one boss that needs to be hit by frost damage to freeze it), many have resistance or immunity to their own type (so fire is ineffective against black dragons or fire elementals etc.), and there are items and spells that boost resistance to a school. Holy damage, has no resistance score. To compensate for this holy spells mostly deal less damage. It is very important for paladin tanks, who rely on being able to damage everything to keep opponents focused on them.
 * Warcraft III also had chaos damage, which ignored all resistances and damage reduction effects. This was however mostly referred to the Burning Legion, and the only unit players got to control (outside of the single-player campaign) that did chaos damage was the summonable Infernal and the Demon Hunter's ultimate form, both of which only lasted a limited time.
 * It ignored armour type (usually). Armour still reduced damage from chaos armour. It would still be better to use magic damage agaisnt heavy armour.
 * Don't forget about the campaign-only Divine armor type used by some bosses. Whoever has it is invulnerable to everything except chaos damage. When it appears, either the boss in question isn't supposed to be killed or (in one instance) something else is needed to gain the ability to kill it; so yes, Divine armor is a honest-to-God Plot Armor.
 * "Shadow" element in Azure Dreams. Belongs only to the legendary monster that becomes available in the epilogue. It is denoted by a picture of a triad containing the three conventional elements that apply to every other monster in the game. Technically, it is neither strong nor weak against anything, but its only spells are ridiculously overpowered, rendering you invulnerable or allowing you to autokill enemies of any strength.
 * City of Heroes has "electrolytic" damage that is only dealt by one particular end-boss.
 * Psionic damage used to be this. Very few armors or defenses protected against it, Invincibility toons were weak to it, and it carries all sorts of Standard Status Effects to disable Defenders. New armors and defenses protect against Psionic attacks, and Defenders have powers to resist status effects in general.
 * Toxic damage used to be an enemy-only damage type (and pretty rare, to boot), but there was nothing in the game that provided any protection from it, much like electrolytic damage. This changed fairly early in the game's run, when Toxic damage was added to the Spines power set's attacks, and Toxic Resistance was added to a large number of defensive and support powers. And even with that change, there is still no power that grants Defense (Co H's dodge chance) against Toxic damage (at least not specifically).
 * The Void Hunters used to deal special "Nictus" damage, which (in addition to being super effective against Kheldians) was also impossible to resist. It was eventually replaced with the already established Negative Energy damage, allowing non-kheldians to resist it normally.
 * Bleach 3rd Phantom has bosses using an "All" element, which behaves like this.
 * A Bonus Boss of Final Fantasy VII has a special "untyped" elemental attack. Of course you can protect yourself against it with the right materia configuration.
 * The Alexander materia is the only holy elemental attack available in the entire game, and is also difficult to find.
 * Entering Fury mode in The Legend of Spyro: Dawn of the Dragon allows both Spyro and Cynder to use a special "Fury Flame" Breath Weapon. It has no particular element, and does a lot of damage to the Elite Enemies specifically.
 * Similar but not identical: In Final Fantasy Tactics, every unit has a zodiac symbol; each unit will take less or more damage from other units at various places along the zodiac. And then there's the Bonus Boss Elidibs, who is the only unit with the Serpentarius zodiac symbol (an actual pseudo-zodiac constellation more commonly known as Ophiuchus) which has no affinity with any other. In addition, he has a special summon called Zodiark, which is Non-Elemental.
 * Zodiark, representing the thirteenth zodiac symbol, also shows up in Final Fantasy XII and its sequel Final Fantasy XII Revenant Wings. They don't have the same gameplay effect there, though.
 * Most Final Fantasy games have a "holy" element that works like this. Generally speaking next to nothing will resist, absorb, or be immune to it, a number of enemies will be weak to it, and it'll only be available through a end-game spell, one or two summons, and maybe an Infinity+1 Sword.
 * One notable exception is Final Fantasy IV. After he becomes a Paladin, quite a few of Cecil's weapons have the Holy element to them. Likewise, the Holy spell returns and forms most of the offensive output of the White Magician Girl, and even the Black Magician Girl can get in on the sacred action with her Dragon summon, stronger than most of her other elemental summons and available once she permanently joins the party. Holy-elemental arrows for the bow users are available very early on, and even The Lancer finds himself with a holy spear as well. Even the ninja has access to the Throw command, so he can just chuck the spears, knives, and swords that the other party members aren't using anymore, sometimes For Massive Damage since Throwing Your Sword Always Works.
 * Most FF games also feature the "Ultima" spell, which often deals the Damage Cap on casting. Like Holy, it's an end-game spell, but there are no known examples of Ultima-resistant monsters. Its prodigious power is often offset by a ridiculous mana cost.
 * In Final Fantasy XI, all elements follow Elemental Rock-Paper-Scissors, but the distribution of elemental spells and abilities is highly skewed. Light and Darkness-elemental abilities that actually deal damage are rare among players, as per typical Final Fantasy thoroughfare.
 * Perhaps the best example of this trope would come in the form of skillchain properties. As skillchains increase in level, they take on more elements and become more devastating. The ultimate skillchain, Cosmic Elucidation, represents all 8 elements simultaneously, hits For Massive Damage, and is only wielded by one boss in the entire game. It currently cannot be executed by players. It also has an additional effect of ejecting your party from the fight, resulting in an automatic loss.
 * In Fire Emblem, while dark magic always factors into Elemental Rock-Paper-Scissors, it is the most damaging form of magic, and very few playable units can use it. Especially in Radiant Dawn, where the only 2 characters that can use it are available only from the second playthrough onward, and even then only during the last part of the game. Some games even go so far as to make it enemy-exclusive, and Path of Radiance completely left it out.
 * While rarity is certainly a point, dark magic is only the most powerful in terms of brute force, taking the same place in the magic triangle as axes do in the weapons triangle, strongest in terms of brute force, but slow and heavy, being weak against the faster but weaker light magic/swords and strong against the average anima magic/spears.
 * Fire Emblem IV - Genealogy of the Holy War had Fire, Wind, and Thunder as the three rock-paper-scissor elements that made up the magic triangle. However, it also had the rare Light and Dark elements, which beat all 3 common elements and were neutral to each other. Only 4 Light tomes exist in the game, one of which can only be used by one character for the very last boss. Dark tomes were enemy-exclusive.
 * Dinosaur King has the Secret element. Unlike the other elemental types, they don't tend towards any specific dinosaur group, and have diverse powers (Eoraptor, for example, can use every move card). Eoraptor is the reward for obtaining the 72 main dinosaurs, the others are not available outside of hacking or special events.
 * Yggdra Union has this in spades. So, swords beat axes, which beats spears, which beat swords. All three of these weapons beat bows, bows beat magic, and magic beats these three weapons. ...and the Big Bad has SCYTHES, which are strong against the three main weapons and weak against NOTHING. Before you ask, yes, only he can use them.
 * Except in the PSP remake, where you can recruit a sweet little housewife with a gardening scythe. SHE IS JUST AS STRONG AS DRAGON RIDERS.
 * Don't forget Durant and his pet dragon! He can upgrade to Gulcasa's class, too, with it. So guess what happens to other enemy units in the game?
 * Kingdom of Loathing has three: Slime in the Clan Bonus Dungeon The Slime Tube, and has a bunch of items in the Tube that affect slime. there's also Shadow, used by your shadow, which is damage immune but takes damage when you heal yourself. Then there is finally Bad Spelling, which take damage when you read the dictionary to them.
 * Legend of Dragoon has two of these. One is literally Non-Elemental, which is neutral to everything and exists mainly in item form, except for one battle. The other is Thunder, which is also neutral to everything, but has a Dragoon associated with it by the end of Disc One.
 * Alter AILA has a somewhat different Elemental Rock-Paper-Scissors with its normal/fire/electric weapons. Nominally, everything should be slightly weak to the fourth element "Psi," though it doesn't work out that way in practice.
 * The Disciples line of games has the standard elements (Fire, Earth, Water, Air, Physical, Mind), and various creatures have resistances to each of these. There are 2 more elements however. Death is an Infinity-Plus-Or-Minus-One element. It's only available to 1 of the factions, which is almost entirely Undead, and thus immune to Death attacks, the Minus-One comes in when you have Undead vs. Undead fights where it's worthless. There is NOTHING immune to the last element Life, and only the capital guardians and the odd campaign boss use it. (The healing units technically use Life, but they heal your guys, they can't cause any damage)
 * The later Castlevania games can be like this with the Holy/Light elemental. It's not that it is broken in and in itself, considering it depends almost entirely on the enemies you fight and some DO resist it, it's that over half of the enemies ARE weak to it. In the Sorrow games, Holy damage is also pretty uncommon for Soma to come by. Most things that resist Holy don't take much damage, or are weak to Dark, that isn't too hard to get. Additionally, aside from bosses, Holy-resisting enemies don't take many hits, or it's a monster that resists EVERYTHING.
 * As per series standard, Holy was intended to be this in Final Fantasy Tactics a 2. In practice it didn't really work that way: While almost nothing resisted it, there wasn't a whole lot weak to it either (and non-elemental spells were easy to acquire). And to make up for its theoretical strength, all of the attacks that used it were weaker than usual. So it kind of sucked. The real ultimate element was wind, which was actually resisted by fewer enemies than holy, had near half the monsters weak to it, perfectly powerful attacks, and was easy to acquire.
 * Luminous Arc 2 has, which universally resists everything.
 * In Epic Battle Fantasy Bomb in the third game. There are huge stretches of the game where almost every enemy is weak to it, and almost nothing actually resists it except a few fire enemies; most importantly it is the weakness of every clay and golem enemy, who otherwise rarely match in the elements they aren't immune to, and all three monoliths, which each are immune to all but two or three types. Lance gets two bomb weapons and two bomb specials regardless of weapon, and they'd all be solid choices even without the element. In the hands of enemies it's nothing special, except that only four items resist it and it can be hard to recognize.
 * In Vattroller X, the weapons owned by the guest characters have no type. This means that once you insert their passwords and buy them, you can equip them as soon as possible, especially because save slots share equipments.
 * Plain old boring Fire is this in Skyrim. Cold is resisted by the most common race (Nords, faux vikings) and enemies (Draugr, undead Nords) in the game. Lightning has the benefit of depleting a magician's magicka reserves, but the vast majority of enemies are not magic users. Fire causes all enemies who are on fire to take extra damage, is the weakness of quite a few Demonic Spiders, and only a handful of enemies resist it. Fire is far and away the most useful despite being no harder to obtain than the others.
 * Angband has quite a few powerful elemental types, such as Time, Gravity, Nexus, Chaos, and Nether. However the crowning example would be Mana, which unlike the others cannot be resisted.
 * Glory of Heracles has the standard four elements, Fire, Earth, Lightning, and Water, which have a cycle of resistances/weaknesses, but then there is the Dark element, which is strong versus all of them! And on top of that, there's the Light element, which is strong versus Dark.

Manga and Anime

 * Most continuities of Digimon utilize a simple triangle--Vaccine beats Virus, Virus beats Data, and Data has higher average stats than the other two (effectively beating Vaccine by default.) However, Digimon Tamers introduces as its final villain a being that doesn't fit any of the three types, and is strong against them all. The protagonists wind up having to change the type designation of their own Digimon in order to fight it properly.
 * Played with in Yu-Gi-Oh!. The Egyptian God Cards (and in the 5D's anime, the Aesir) are DIVINE-Attribute and Divine Beast-Type, which more reflects on their status as Physical Gods than conferring any innate gameplay benefit. In fact, even though the Egyptian God Cards now have official tournament-legal counterparts, they're not very playable because of their unique Attribute and Type, which means they have no support whatsoever (unless you count Horakhty the Creator of Light, a game winner which can only be summoned by Tributing the three).