Yin-Yang Clash

Two forces exist within the same 'Verse. Both of them are unbreakable absolutes. And they are diametric opposites.

Naturally, this raises one question in everyone's mind: What happens when they fight? Sometimes the story itself will depict the fight, sometimes characters will simply speculate about the fight, and sometimes the story won't address the issue at all, leaving the fans to debate amongst themselves what the outcome would be.

There are several possible outcomes:
 * One or both of these forces proves less absolute than advertised:
 * Yin is stronger and defeats Yang (or vice-versa).
 * Yin and yang both destroy each other simultaneously, an outcome that's both a win and a loss for both sides.
 * Both forces are completely evenly matched, so they clash forever or until some outside force intervenes.
 * Both of the forces are absolute, so the logical contradiction of their fight destroys the universe.

In the West, the Unstoppable Force Meets Immovable Object conundrum is the most famous version of this, enough so that it's become a Stock Phrase. The Eastern equivalent is the unstoppable sword and unbreakable shield (see Folklore, below)--the Chinese word for "contradiction" is derived from this.

See also the supertrope Ultimate Showdown of Ultimate Destiny.

Please note: This is for actual, absolute forces. See Unstoppable Force Meets Immovable Object for the use of that particular stock phrase to refer to objects or people who aren't absolutes.

Anime and Manga

 * This may be what happened in the second Tengen Toppa Gurren Lagann movie, Lagann-hen, when the Super Tengen Toppa Gurren Lagann and the Super Grand Zamboa launched their Giga Drill Breaks at each other. The universe did collapse, at least.

Comic Books

 * The X-Men foes Blob and Juggernaut are sometimes portrayed as this. (Juggernaut's superpowers boil down to being an Unstoppable Force, and The Blob's powers boil down to being an Immovable Object.) Though other comics have stated that The Juggernaut would simply win.
 * The other comics that depict Juggs the winner go with the fact that he's a mystically-empowered human, and not a mutant like the Blob. So it's more/less "mystic powers vs. mutant abilities".
 * This is invoked by name in a Superman comic in which Superboy travels forward in time—Superman is the irresistible force, Superboy the immovable object. The result is that Superboy gets sent back to his home time.
 * Another example comes courtesy of Grant Morrison's All-Star Superman. His solution? "They surrender."
 * The finale of Alan Moore's Swamp Thing story arc "American Gothic" ends like this. A group of male witches awaken "The Great Evil Beast," perhaps the ultimate Eldritch Abomination, as it the complete and total absense of God's light, with the intention of destroying not only the universe but heaven itself. As it slowly moves forward, Etrigan, The Spectre, and Doctor Fate all try and fail to defeat it. Finally,  If that sounds like a massive Mind Screw, it's because it is.

Fan Works

 * The "Event", found in the Void Between the Worlds in the seminal Self Insert fic series Twisted Path by Darren "Twister" Steffler, is a titanic confluence/battle of the forces of Mind and Magic. Getting thrown in it to get rid of him -- because of course No One Could Survive That -- instead empowers Twister to a near-godlike degree.

Films

 * The Matrix: Neo vs. Agent Smith.

Folklore

 * A classic example comes from the Han Feizi. A merchant selling spears and shields claims that his spears can pierce anything and his shields can't be broken. When someone asks him what would happen if he were to strike the shield with the spear, he is unable to answer.

Literature

 * Peter Crowther's "The Eternal Altercation" features a train in which the (identical looking) embodiments of Hope and Dispair are locked in eternal combat. The train operator's job is to jerk the train if either of them gain too much ground.
 * Forgotten Realms spin-a-yarn story "The Night Tymora Sneezed" had a codpiece that "awakens battle-lusts and... lusts in general" and a chastity that aids "[...] in resisting the distractions of the flesh and dedicating themselves wholly to the clear-headed vigilance the Supreme Guardian demands". Hilarity Ensues, of course.

Oral Tradition, Myths and Legends

 * In Greek Mythology, Amphitryon once sent Laelaps, a hound that can catch anything, after the Teumessian Fox, which can never be caught. Zeus's resolution to the paradox was to turn both animals to stone.
 * Actually inverted by original Taoism, where Yin and Yang are not opposites, but compliments of each other. What is perceived as a "conflict" or "struggle" to keep the forces balanced is actually the two of them working in harmony. Furthermore, the clash of Yin and Yang, if it can be called that, is actually a good thing, as the ineffable Tao is formed and supported by the two absolutes working with each other.

Tabletop Games

 * Dungeons and Dragons 3rd edition actually has a lesser known rule that solves this problem if you look at as the "spear/shield" version. In D&D specific trumps general, and thus the spear that can break any shield (specific power to break shields) trumps the shield that can't be broken (general power to be unbreakable).
 * Since Exalted contains a lot of 'irresistible' and 'invincible' powers, they do have a rule for this. A perfect defense always wins, even against a perfect attack. Always.

Video Games

 * Shield and Sword from Suikoden: Shield can withstand anything, and Sword can destroy anything.
 * The Han Feizi story is retold in Phoenix Wright: Ace Attorney. The "King of Prosecutors" trophy is a broken shield and knife, showing the result of the truth being pursued to its conclusion.
 * One mini-boss in The Legend of Zelda Oracle Games is defeated this way. You have to trick it into hitting its unbreakable shield with its unbreakable sword to destroy both.
 * The Iron Clefts in Paper Mario: The Thousand-Year Door claim that their bodies can withstand any attack and their spikes can pierce anything. To defeat them, you have to knock them into each other with Yoshi's Gulp attack.
 * In Pokémon Ruby and Sapphire, it's Groudon (representing the land) vs. Kyogre (the sea). Rayquaza the sky dragon needs to step in to break them up. (When pitting the two against one another in actual gameplay, Kyogre has a clear type advantage, but Groudon has an ability and movepool that's potentially well-equipped to deal with water-types.)
 * Pokémon Black and White takes this a step further: the version mascots Reshiram and Zekrom are literal embodiments of yang and yin. They are this whenever they meet each other in battle, so much so that This also makes it so that the side that wins is dependent upon version (Yang wins in Black, Yin for White.)
 * In Fate/stay night, Lancer's ultimate attack uses his cursed spear Gáe Bolg to pierce his opponent's heart without fail before he even starts the attack. In the Unlimited Blade Works route, he throws the spear at Archer for even greater power. Archer responds with Rho Aias, a legendary shield that no spear was ever to pierce.
 * Asura's Wrath has

Web Comics

 * Brawl in the Family shows us what happens when Kirby and Pac-Man both try to eat each other.

Web Original
"Since all tests thus far have shown that neither SCP-225-1 nor SCP-225-2 can be damaged or moved by any means known, the possibility also exists that neither object would be annihilated, halted, or altered from their course even by contact with the other. If this is true, then a collision between SCP-225-1 and SCP-225-2 has the potential to . In this circumstance planetary evacuation may not be sufficient"
 * Uncyclopedia: Both Mr. T and Chuck Norris are depicted as Memetic Badasses. According to one article (which has since been deleted or edited into oblivion) the fight between the two of them resulted in the Big Bang and the creation of the universe.
 * Accordingly, some people joke that the biggest reason cloning should be outlawed is because cloning [insert name of your favorite Memetic Badass here] would make one of these possible.
 * The winner of the October 2002 Animation round of The Internet Ray Tracing Competition (topic: Force) had some fun with the concept.
 * Encyclopedia Dramatica: Longcat vs. Tacgnol.
 * The SCP Foundation deconstructs it with SCP-225, a pair of objects, one unstoppable, the other immovable, both indestructible. The Foundation has no idea what would happen if they collided (though a multi-gigaton nuclear explosion has been speculated), and they really don't want to find out. Worse, they have no known way to prevent such a collision if it were going to occur, since neither object can be affected by anything.