The Group

Basically, a sub-trope of Names to Run Away From Really Fast that applies specifically to a group or organization, as well as the Super-Trope under which several others fall (such as Ancient Conspiracy and Government Agency of Fiction).

The Group does not have any proper nouns in its name. This is meant to convey just how ancient, mysterious, clannish, secretive, powerful, and connected it is. It is not "The Silford Group". It is simply...The Group. The Group is typically some form of Ancient Conspiracy, Government Agency, or Very Powerful Crime Syndicate. Even more likely, The Group will be some combination of some or all of the above, such as an ancient and extremely highly-trained order that traces its origins back to the time when it was an Egyptian mystery religion, today has deadly assassins and The Men in Black counted among its many agents, is technically an ancillary part of the United States government and, oh yeah, manages a large underground criminal empire as well.

If there's a Masquerade going on in your world, The Group is, de rigueur, the first ones in and the last ones out to deal with anything related to it. If it gets broken, that's on them. Even if The Group is evil, which they may well be, they may often try to cover up The Masquerade in an attempt to utilize whatever it is for their own ends, and thus do the world some good by keeping it ignorant and safe. Whether it is mystical, supernatural, or horrific beings, creatures, phenomena or MacGuffins, things of alien origin, superhumans and related paraphernalia, examples of advanced technology, time travelers and the difficulties they create, various types of monsters, demons, or whatever other Green Rocks or Weirdness Magnets may be around in a world, you can be assured The Group will be there to either hunt and destroy them, try to manipulate and use them, or simply watch and contain them. Oh, and it should go without saying that if anyone is in charge of The Group, yes, it will be an Omniscient Council of Vagueness.

It's also entirely possible to have two Groups in the world. Often, they will be fighting a war in the shadows, this will be the basis for an Arc (story or myth), typically with one fighting behind the scenes to protect the world, and the other secretly trying to destroy or corrupt it. The Group may be several decades old (for example, formed around World War II or the Cold War), several hundred years old (for example, dating from around the time of the Industrial Revolution and the American and French Revolutions), several thousand years old (originating in Ancient Rome, Ancient Greece, or Ancient Egypt), as old as human civilization itself (as soon as one cavemen invented fire, two others got together on the other side of the cave and whispered to each other that they had better keep an eye on this, and thus The Group was born), or older than time itself (humans may serve The Group, but some very definitely non-humans founded, and control, it).

Anime & Manga

 * Cowboy Bebop also has The Syndicate.
 * Les Soldats from Noir technically counts, since it's just French for "The Soldiers". It's also a textbook Ancient Conspiracy.

Comic Books

 * The Authority.
 * The Boys.
 * The Enclave: A group of criminal scientists in the Marvel Universe.
 * The Committee: A criminal organisation from the same.
 * The Conclave: The Avengers foes. A shadow cabinet made up of members of every U.S. government organization.
 * The Corporation: Nationwide business-like criminal organization. Foes of Captain America (comics) and The Incredible Hulk, amongst others.
 * The Cabal, a group of several powerful supervillains and antiheroes, and Evil Counterpart to The Illuminati.
 * Magento's organization was just called The Brotherhood for a while. After it abandoned The Brotherhood of Evil Mutants
 * The Fraternity from Wanted; while the movie has an organization of Anti-Hero Jerkass assassins, the original comicbook has full on amoral supervillains.
 * Sin City has "The Guild", a group of assassins who also deal in the Black Market.

Film

 * The Division in Push.
 * The Order from Sherlock Holmes are a No Celebrities Were Harmed version of the Freemasons as they were commonly thought of in Victorian times, being a shadowy group of influential men at the highest reaches of power engaging in mysterious, weird rituals. It's gradually taken over by a powerful and charismatic Dark Messiah who has returned from the dead and is demonstrating his power to such an extent that almost the entire country is utterly terrified of him. However, it's ultimately a complete deconstruction, as the Order is largely presented as a bunch of superstitious and largely ineffectual old men who are utterly caught up in their own mythology . It's also an excuse for them to have orgies, apparently.

Literature

 * Nineteen Eighty-Four has The Party. (It also has The Brotherhood, but they're not working against the protagonist.)
 * In the Anne Rice books, it's The Talamasca. "We watch, and we are always there."
 * Bently Little has a whole slew of novels like this. The Store, The Association, etc. They are all horror.
 * The Organization from Fearless.
 * The Majestic 12 from Scarecrow, the 12 richest men who secretly run the world for their own profit.
 * An earlier Matthew Reilly book Area 7 had Die Organisasie (The Organisation in Afrikaans), a group of South African leftovers from Apartheid.
 * The Shop, from Stephen King's Canon Welding crossover-verse which ties all of his fiction into the Dark Tower universe.

Live Action TV

 * Lost has both The Others and The Initiative.
 * The Committee from VR.5.
 * The Dominion from Deep Space Nine has the right sort of name (although, so does The Federation, come to think of it), and they were definitely a mysterious powerful organization in the first few seasons. Section 31 is the clandestine intelligence agency in the Federation that has been around from the beginning. The Circle was a short-lived Bajoran political party/terrorist organization/Cardassian front.
 * The Centre, of The Pretender.
 * Wild Palms: The Fathers.
 * Heroes. The Company.
 * The X-Files. The Syndicate.
 * The N.I.D. in Stargate SG-1. According to the RPG sourcebook it stands for National Intelligence Department.
 * And later, the Trust.
 * Bureau Thirteen in Babylon 5. Heard of once in the episode Spider In The Web, then never heard from again.
 * Alias had the Alliance and later the Covenant.
 * Arguably parodied by the Agency from the Syfy's series The Invisible Man. It's a secret government agency that consists of about five (visible on-screen) people, and because of this is prone to being transferred around between various departments of the US Government, as well as suffering from budget cuts. About the only thing they have going for them is that the titular invisible man works for them.
 * The Ring from Chuck.

Tabletop Games

 * The Agency in Deadlands.
 * The Directive, a shadowy intelligence organisation from the Aberrant role playing game.

Video Games

 * The Cabal in Blood. Known more properly as the Cult of Tchernobog, but more often called just Cabal.
 * The Club.
 * The Conduit has The Trust.
 * The Enclave from Fallout
 * The Exchange from Knights of the Old Republic.
 * The Order in Freelancer.
 * City of Heroes / Villains has The Family.
 * And the Council, the Cabal, the Banished Pantheon, the Lost, the Minions of Igneous and the Midnight Squad.
 * The Hitman videogames have the International Contract Agency, which is usually known as just The Agency. Although they're the organization the protagonist works for, they're morally ambiguous enough to count. A competing group is The Franchise. In the movie the group is called The Organization.
 * The Organization from Street Fighter III, a strange, powerful cult that has produced the superhuman Gill, is never really given a name in the Japanese, though it is sometimes referred to as the Illuminati in English.
 * The Agency from the Syphon Filter series of games, which served under The Consortium. After, it gets reorganised into the International Presidential Consulting Agency... which still doesn't have any proper nouns.
 * The Foundation in The Suffering II: Ties That Bind, which seems to be a paramilitary organization hell-bent on . They also have an unhealthy interest in Torque,.

Web Original

 * The Guild.
 * In the SCP Foundation universe, the titular organization is often referred to as simply "The Foundation."
 * One of the groups opposing them is called The Factory.

Western Animation

 * On Phineas and Ferb, the organization Perry the Platypus works for is known simply as The Agency. Word of God has it that it's actually called O.W.C.A., the Organization Without a Cool Acronym.
 * The Centre from Martin Mystery is a clear cut heroic example.
 * On Ben10, the Forever Knights were originally called The Organization.

Real Life

 * The Company (referring to the CIA) and The Bureau (referring to the FBI). Of course, only used when their motives are secret...
 * The Farm is where the The Company trains its agents.
 * Real Life musical groups The Group and The Band.
 * More meta: The The.