State Sec(urity) is a civilian agency or political entity that has its own paramilitary forces. It could be official or unofficial, but it exists to enforce an ideology or support the government. Its something akin to the Secret Police, but on steroids. Often the organization is on the side of evil, but this is not always the case.
The most powerful versions are autonomous from the regular government and military. They tend to be vast organizations - the secret agents and cloak and dagger stuff are but one subset. Other divisions can include a full-blown paramilitary division to keep the regular army in check and act as a regime protection force, a political and administrative division, a propaganda division, an R&D division, you name it. And to make sure State Security stays loyal, there could be an elite force within the organization to keep it in check.
The trope gets its name from the Honor Harrington book series, where State Sec has its own Space Navy, Space Marines, Army, various intelligence organizations, etc... This was in turn inspired by the Real Life Schutzstaffel of Nazi Germany, which had the elite Waffen-SS which was pretty much a second German Army for the Nazi party, the Allgemeine-SS which ran the damn thing, and many more. A full list can be found at Wikipedia. Needless to say, this trope tends to coincide with Putting on the Reich a lot.
Also, it's very common in Real Life and has been seen throughout history. Political intrigues and favoritism can lead to Interservice Rivalry with the Regular Army. Mega Corp. and N.G.O. Superpower are when corporate or other non-governmental entities wield similar levels of influence, infrastructure and paramilitary power.
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Media in General
In general, if The Spanish Inquisition (or a group along similar lines in fantasy) shows up in media, it's likely going to be one of these.
Anime & Manga
Hellsing - In the anime, the titular anti-vampire Organization has a paramilitary vibe. The group has a number of well armed, equipped, and trained soldiers used to take out said vampires. Contrasted in the manga and OVA, were the troops are limited to being the Red Shirt Army.
The Gundam franchise seems to have something of a love affair with this trope. Some notable examples include:
The Titans, the main antagonists of Mobile Suit Zeta Gundam. They eventually take over the regular Federation Forces and become a de facto military dictatorship. They manage to be even more Nazi-like then their predecessors, the Principality of Zeon from Mobile Suit Gundam (ironically, their original stated purpose was to eliminate Zeon remnant groups).
The Titans are replaced following the First Neo-Zeon War with Londo Bell, which, since it is run by Bright Noa, is a far more moral example that doesn't abuse its authority. That said, it is still an autonomous military force outside the regular chain of command, with its official mission statement being to hunt down Zeon upstarts.
The A-Laws (Autonomous Peace-Keeping Force) from Mobile Suit Gundam 00, who are obvious expies of the Titans. They're autonomous from the regular military, with access to secret police, and under the direct command of Ribbons. Interestingly enough, the organization had different levels of trust: Those who have no idea what the A-Laws are really doing, the ruthless top brass who knew what the A-laws were doing but remained mere pawns, and the Innovades who really knew really what was going on.
The Organization of the Zodiac in Mobile Suit Gundam Wing is an interesting case, zig-zagging as the series went on. While officially part of the Alliance military as a elite force, it was secretly the Romefeller Foundation's military wing. After eliminating the Alliance, OZ becomes the regular army for the Romefeller government.
Phantom Pain in Mobile Suit Gundam Seed Destiny is a downplayed version - it's a special forces group used to support the radical Blue Cosmos faction. They get to use advanced (but illegal) technology, has skilled personnel, and are autonomous from the regular chain of command. But despite being used to expand Blue Cosmos' and LOGOS's agendas, the group mostly uses standard Alliance uniforms and don't seem to be ideologically charged as other examples.
Black Cat has Chronos, a world-wide peacekeeping organization that amongst other things has a division of elite assassins (which the main character Train was once a part of), units of special forces troops, a world-wide intelligence network and multiple R&D divisions working on various research projects (like nanotech).
Phantom in Innocent Venus specializes in putting down "rebellions", which basically means help the plutocracy oppress the poor. With Humongous Mecha.
Rare heroic example in Ghost in the Shell, as the protagonists are part of Public Security Section Nine. They operate with great autonomy, are only ever seen reporting to the Prime Minister or the Minster of Home Affairs, regularly violate laws which would bind other governmental organizations, and thanks to virtually no oversight, almost never get caught doing so. While Section Nine itself is only a small elite team of mostly ex-military operatives with a small support staff and a lot of cutting-edge equipment, they are still only one of at least eight other Public Security Sections, each with a different structure and area of responsibility
NERV from Neon Genesis Evangelion. They are not only funded directly by the UN (but actually controlled bySEELE), they have special legal protection and are the sole organization operating Evas. There was one instance where an American admiral was forced to cooperate by a NERV captain which shouldn't be possible in real life; in another example, the same captain requested a prototype weapon from the Japanese military and immediately got it without any red tape. It is said that their expenses involving Eva repairs and collateral damage could immediately bankrupt a small country. They also happen to have an Elaborate Underground Base as their main headquarters, a Captured Super Entity in the basement, as well as control over an entire city.
Kerberos of Jin-Roh: The Wolf Brigade are paramilitary police forces wearing iconic "Protect Gear" and armed with machine guns. Officially part of the Metropolitan Police, which has political clashes with the Capital and Self-Police, among others.
The recently created Alpha Lanterns of the Green Lantern Corps fit this trope. Created to act as an Internal Affairs force for the GLs, they are armed with two power rings, made into cyborgs with Manhunter technology that allows them to drain other rings of power, have built in power batteries to negate the need to recharge, and have their personalities erased in favor of a direct mental link to the Book of Oa and Central Power Battery, thus removing any impurities which may color their interpretation of the Guardian's laws. Which may prevent them from becoming Knight TemplarWell Intentioned Extremists powerful enough to take down the entire GLC (seriously, with the rest of that description they're practically asking for it), but doesn't make the Guardians look particularly heroic...
As it turns out, hasn't prevented that at all, especially not with Cyborg Superman taking control of them. Earth's GLs, quite understandably, gave a collective What The Hell Guardians somewhere between "Manhunter technology" and "personality erased". (Although the Alpha Lanterns themselves insist their personalities haven't been erased, just intensely focused; but then, they would think that, wouldn't they?) Their extreme resemblance to the Manhunters shows that even when you are semi-omniscient and immortal, you can't learn from history.
And then in Final Crisis, Granny Goodness possesses Alpha Lantern Kraken, captures Batman, and tries to steal the Central Power Battery. Real infallibe, and Hal Jordan points it out.
S.H.I.E.L.D. from Marvel comics is a intelligence and counter-terrorist agency, that has some pretty spiffy military hardware, including a flying aircraft carrier armed with an ICBM and a squadron of jets.
In Aeon Natum Engel and its rewrite Aeon Entelechy Evangelion has a such efficient State Sec that it makes the state sec of the source material, Cthulhu Tech, look downright lazy. It also makes the "Everything is falling apart" scenario from the latter's sourcebooks impossible.
In Starcrossed, it is revealed that Section 31 actually has a powerful fleet of warships... real warships, not the normal Federation universal purpose vessels. They get a few shots at the invaders, but generally suffer rather badly from the Worf Effect. Also a bad case of What the Hell, Hero?.
True to the games,Tiberium Wars portrays the Brotherhood of Nod's Black Hand as this. They're a separate army that operates under its own command structure, answering only to Kane. One of the GDI intelligence reports states that Black Hand units are dispatched to troubled areas with civil unrest to reestablish order, among other things, and Black Hand officers of significantly lower rank are able to overrule high-ranking Nod officers.
The Uplifted series explores the personal side of the rivalries held between the Wehrmacht and the SS, both of whom have nothing but contempt for the other group. The writer doesn't play favorites, having a prominent Prussian call his protagonist a "Well dressed ditch digger." Ouch.
Fallout: Equestria: Applejack's Ministry of Wartime Technology created the Steel Rangers, a force of Power Armor equipped soldiers that fought alongside the Royal Army and later became the analogue to Fallout's Brotherhood of Steel. Not to be outdone by her old friend, Twilight Sparkle's Ministry of Arcane Science attempted to create their own force of alicorndemigoddesssuper soldiers, which backfired horribly, creating the analogue to the Master and the Super Mutants.
The Office of Special Resources in The Universiad, The UnfetteredToken Evil Teammate who tick off most of the criteria on the list. They are outside and above the chain of command of the Forum's official military services. Their leader reports direct to the Moderators. As the name suggests, they have the final word on Forum resources. They have their own intelligence and R&D arms and their technology and training is far beyond all the rest, such that even an OSR "grunt" is superior to most other Forum special forces. Only their comparatively low numbers prevent any coup attempt from being a Curb-Stomp Battle, and even then heavy casualties are expected.
The Intelligence and Reconnaissance Department (IRD) is the state security of the Demon Empire in Sonic X: Dark Chaos. They are outside the military and follow only Beelzebub's orders. The Erelim is a more benign version of this for the Angel Federation.
The Immediate Action Organization in Alternate History film It Happened Here, a tale of Britain under German occupation with a Vichy-style government. Also represented are the Blackshirts, the Real Life British Fascist counterpart to the German SA (Brownshirts).
The Special Police Force in Sleeping Dogs that is established to counter guerrilla activity when civil war breaks out. They were blue uniforms and berets, working alongside ordinary army troops in a paramilitary capacity.
S.H.I.E.L.D. of the Marvel Cinematic Universe - A intelligence agency with it's own research faculties, a flying aircraft carrier, nukes, and personal connections with the Earth's superheroes.
The Rehabs of RoboCop 3. These "Urban Rehabilitators" are supposed to help augment the Detroit Police in fighting crime. In reality, they're cold blooded mercenaries that force people out of their homes and wipe out any resistance.
In Star Trek Into Darkness, it's implied that Section 31 under Admiral Marcus is trying to become one of these - having developed its own weapons and privately operating a unregistered, powerful warship. In addition, it's personnel have their own distinct uniforms, and operating to advance Marcus' own agenda.
After the fall of the People's Republic, many State Sec warships flee Havenite space, becoming Former Regime Personnel. Two are destroyed by HMS Hexapuma in Shadow of Saganami. Those two, along with many more, were hired by Mesa, and eventually sent against Torch. They failed thanks to the intervention of Commodore Luis Roszak, whose Solarian forces took a serious pounding.
The Culture has Contact and Special Circumstances, which nominally act as its diplomatic and secret services. During wartime, both groups serve the Culture in a military capacity.
Vorkosigan Saga - The Barrayaran Ministry of Political Education. Emperor Ezar's right hand during much of his rule, they thought themselves to be the power behind the throne, until Ezar made them one of the scapegoats for the failed Escobaran invasion. His left hand, Imperial Security, is a much more constrained organization wholly dedicated to the continuation of the Barrayaran Imperium, but also bound in what they can do by Barrayaran tradition.
Implied in Vengeance for Nikolai by Walter M. Miller Jr. America is taken over by a fascist government which starts a war with the Soviet Union. Separate from the Army are the Blue Shirts, who are overly nationalistic and brutal in their interrogations of Soviet POWs.
Dreamland from Dale Brown books are a top secret USAF unit who, while sometimes seconded to regular commands, frequently act beyond the remit of the conventional military, engaging in black ops around the world with the aid of Cool Planes and other advanced technology. In their Night Stalkers/Sky Masters, Inc./Scion/Whatever-it-is-today incarnations they are more of a N.G.O. Superpower. They're the heroes, though generally seen as loose cannons by others.
The Iron Guard in Hammer's Slammers is hinted to be this trope. Personally loyal to President-For–Life Van Vorn, the Guard were "political bullies" than actual soldiers.
The Romulans of Star Trek have the Tal Shiar, which not only act as an intelligence agency, but have their own ships and ranking system. Similarly, the Cardassians have the Obsidian Order, which has elements of this trope despite being officially restricted to Secret Police level. Both organizations compete enthusiastically with their government's official military. However, prior to the Dominion War, they worked together to attempt wipe out the Dominion, only to find out the hard way they are fell right into their enemy's trap and got their clocks thoroughly cleaned.
The Tal Shiar did manage to recover from the loss, and continued to have some power on Romulus. The Order, however, was effectively wiped out, allowing the Cardassian dissident movement to return control of Cardassia to civilian authorities.
Averted with the Klingons. Despite being created to serve as a counterpart to the Soviet Union, the Klingons were never shown or established to have their own version of the KGB.
In Expanded Universe, though, the Klingons are revealed to have Imperial Intelligence, which also acts the part of the Secret Police. There is plenty of Interservice Rivalry between the IDF and the II. The former despise the underhanded tactics employed by the spooks, and the latter consider the warriors to be dumb grunts.
The Ferengi's Intimidating Revenue Service has characteristics of State Sec as well, as it is powerful enough to depose the Grand Nagus and its Liquidators often hound individuals for years.
Averted with the shadowy Section 31. While so secret that even the Federation Council and President are (supposedly) not aware of its existence, free from any official government oversight to protectThe Federationat all costs, they don't maintain their own paramilitary forces (their operatives and supporters in Starfleet handles things when a bit of muscle is needed for a plan).
The lengthy Doctor Who serial "The Dalek Master Plan" has Space Security. Although human, and opposing the Daleks and their evil plan, these black-clad paramilitary agents of the year 4000 execute people at the drop of a hat (one even kills her own brother simply because she's been ordered to). Notable for the presence of Nicholas Courtney who went on to play The Brigadier, as well as the fascist 'Brigade Leader' in an alternative universe (Inferno). Ironically Space Security were to be the heroes of the never-made spin-off series Daleks. Another SS-like force are the Kaled guards led by Security Commander Nyder in Genesis of the Daleks.
Babylon 5 had the Psi Corps; and to a lesser extent Nightwatch. The authority of the Psi Corps is officially limited to matters dealing with telepaths. The Nightwatch is a more straightforward example, with them being a purely political organization by the dictatorial Clark regime. Word of God has that Nightwatch even absorbed Homeguard, an well armed terrorist group opposed to alien affairs.
In Kamen Rider Dragon Knight, there is a secret organization called the No Men. Their job includes protecting the world from potentially dangerous aliens and even capture one of the heroes who they feel could be a threat. They've even gone to the length of infiltrating a blogging site to play down the conspiracies that are being uncovered.
The Imperium of Warhammer 40,000, being incredibly vast, has several to varying degrees:
The Inquisition - the original and most iconic of the Imperium's State Sec.
The Adeptus Mechanicus. Technically speaking, the Machine Cult isn't Imperium at all, it's the separate (semi-)independent human empire that just happens to be in personal union with The Emperor himself. The Inquisition is highly suspicious about them, and not always without a reason.
Other notable organizations include the Adeptus Arbites, the Officio Assassinorum, certain space Marine Chapters, and the Adepta Sororitas.
The Ecclesiarchy has the Frateris Militia, as well as the Witch Hunters - who are not to be confused with the other witch hunters, the Ordo Hereticus, who are part of the Inquisition.
The Adeptus Terra operates the Officio Sabatorum and the Templars Psykologis.
The Administratum has the Logis Strategos.
Cthulhu Tech gives us the Office of Internal Security and considering the type of world its in you know that they have to have a lot of firepower.
The Old World of Darkness had the Technocracy, a group of mages that was very much interested maintaining the world's current status quo. Amongst other things it included New World Order Men In Black, cyborg Super Soldiers, genetically engineered monsters and whole bunch of other crap.
Hunter: The Vigil features Task Force VALKYRIE; a paramilitary organization run by the United States government tasked with countering supernatural threats to the America.
Many of the governments in Battletech have such organizations. Some of the most notorious are the Capellan Confederation's Maskirovka, and the Lyran Commonwealth's Loki. The latter almost took over their government.
The Imperial Interstellar Scout Service in Traveller is a downplayed version of this. While most of it's work is done by small groups in the back of beyond, it has a number of hand-me-down Imperial Naval vessels as well as it's own Swat-team style Space Police commandos.
COMPNOR (Commission for the Preservation of the New Order), which basically is the Empire's equivalent of the SS. It has an executive committee, its own military and intelligence wings, a social engineering agency, and its own youth group. The Imperial Security Bureau was notable for its ability to take over entire Imperial Navy Star Destroyers at whim, running the Navy through illegal tests of character without telling anyone, and killing anyone who fails the tests without going through any procedures. Or at least they did... until Vader himself cracked down on them. ISB also had plants on every ship with orders to kill head officers and take over if they mutinied or deserted.
Corellia's Public Safety Service, which used to be the nobler law-enforcement agency the Corellian Security Force.
In some ways, Jedi act this way given the allegiance to the Republic as opposed to simply the light side of the Force. In addition their level of power gives them a fearsome reputation that they are willing to use to their advantage in both TPM and AOTC as "keepers of the peace".
Star Wars: The Old Republic gives us Imperial Intelligence of the resurgent Sith Empire. It was quite possibly the most deadly and feared organization the galaxy has ever seen at the time, responsible not only for intelligence gathering but internal security, with an it's own private army and navy that operated separate of the regular military's chain of command to enforce order on Imperial planets.
In the Command & Conquer games, the Black Hand of Nod fits the trope. It started out as Kane's personal body guard, developed into a religious secret police and special ops group, then eventually became a subfaction of its own. By the Third game expansion, the Black Hand have their own military, political and religious wings, and act as a second army of Nod. Also, it's not a coincidence that it shares the name of the organization that was behind the murder of Archduke Franz Ferdinand, which started The First World War. It's pretty much stated that that was them.
In the manual of Command & Conquer: Red Alert states that the Soviet's NKVD adds 7 million troops to their strength of 14 million regulars. Compare this to the setting's Allies, whose military strength (regular and irregular forces), is about 5 million total at the game's beginning.
The Spectres in Mass Effect. Its not completely apparent how much authority they have over commandeering Citadel military forces to execute their objectives, but it would appear to be absolute. Saren, except for the whole 'not working for the Council', was pretty much a one-man version of this.
The Special Tasks Group are basically the Salarians' version of this, and in fact inspired the Spectres.
The Sentinels of Hallifax in Lusternia are a fantasy variant of State Sec. Amongst other things, the Sentinel Company are elite soldiers, Secret Police and Time Police designed to rein in the many paradox-causing experiments of sister organization The Institute. Hallifax in general encourages this trope as part and parcel of its dual futuristic-Communist motif.
In the Crusader games, SecCart (Security Cartel) handles defense and security for all WEC facilities and personnel. Given the corporate-fascist nature of the game's setting, this means they also handle police, intelligence, and so on.
Shinra's Turks exist in a weird realm between this, normal Secret Police, and The Men in Black, with a pinch of ninja. A Turk operation with SOLDIER muscle thrown in resembles this particularly. That they are the long semi-secret arm of an electric company means they have certain freedom from responsibility vis-a-vis the public and international community that more standard governments do not enjoy, so their structure is somewhat unusual to reflect this.
In The Elder Scrolls series, about the timeframe of The Elder Scrolls V: Skyrim, the Aldmeri Dominion is ruled by a faction known as the Thalmor, who maintain their Nazi-style fascist government by having their own special military branch. Thalmor troops are directly responsible for maintaining the ban on worshipping the god Talos within the Empire of Tamriel and have the legal right to do so thanks to a rather lopsided peace treaty between the Empire and the Dominion signed after a massive war between them.
In Escape Velocity Nova, The Federation's Bureau of Internal Investigation started life as a domestic intelligence agency (maybe akin to MI-5), formed in response to (likely unfounded) public fears of Auroran infiltrators. Within a handful of years (or possibly a handful of decades — there are some apparent contradiction between the Timeline Preamble and in-game texts), it had suborned the entire government, turning the Federation into The Empire, and now operates its own fleet.
Part of the mission statement of the Polaris' Mu'hari caste is to ensure the survival of the Polaran people, whatever the cost. This means that they take on the State Sec/Secret Police role at times by necessity, but since they're treated as benevolent caretakers, this counts as a subversion.
The Office Of Naval Intelligence of Halo either is this, or very close to it. They're a branch of the Navy which operates completely independent of its command structure and can even co-opt the regular Navy and even civilians to do work for them. They don't have a military force per-se, but they operate all the UNSC's stealth ships and operate tons of secret projects, like the Spartan program, which produced dozens of Super Soldiers from kidnapped children for the expressed purpose of fighting rebellious colonists. Their agents are all pretty enigmatic and operate outside the bounds of the law and often without qualms about morality. It has its own propaganda arm. And is powerful enough that its director can greenlight operations kept secret even from its superiors, even if those operations are designed to undermine her government's foreign policy. If it weren't for the Covenant trying to wipe out humanity (and thus, firmly established them as the bad guys), fans might actually take a harder look at ONI's seriously questionable methods.
With the end of the Human-Covenant War and the aforementioned plan to undermine foreign policy, the fans have started looking at ONI harder. And they don't like what they're seeing.
The NSA in Perfect Dark. Unlike its real world counterpart they have their own armed troops and control Area 51. Considering that its director is corrupt and part of a conspiracy it may be that that no one knows about the personal army part.
Endless Space has the Sheredyn, who were originally just the bodyguards for the emperors of the United Empire. By the time of the game, however, the Sheredyn have begun to take over corporations along with building independent colonies and creating their own interstellar logistics networks in addition to their military forces operating outside the Imperial military's regular chain of command. This has transformed them from an elite bodyguard force into a powerful subfaction within the empire; to the point they are almost a state within a state.
Angels 2200: The Terran Office of Special Investigations (OSI).
The Schutzstaffel of Nazi Germany, better known to Westerners by the abbreviation "SS". Particularly notable is that the SS included the Orpo (ORdnungsPOlizei = Order Police), Kripo (KRIminalPOlizei = Criminal Police), Gestapo (GEheimeSTAatsPOlizei = Secret State Police) and Sipo (SIcherheitsPOlizei = Security Police), several of which (at various times) became users of this trope in their own right. It should be noted that the SS were originally only a group of bodyguards and were subordinate to the SA, the brown-shirted stormtroopers. It was only by a series of successful power plays that the leader of the SS, Heinrich Himmler, was able to expand his power base to practically controlling or at least threatening every aspect of German society. The Waffen-SS (literally, weapons SS) were the military wing of the SS, with a separate command structure from the Wehrmacht. However, they were subject to the Army High Command while in the field.
Many historians have gone so far as to call the SS a "state within a state", because at their height they not only had their own police, army, intelligence service, administration of the death camps and the Einsatzgruppen death squads (who gassed over one million Jews). They had their own schools, clubs, a medical corps (which included Josef Mengele), a science corps, a women's corp (which were auxillary, or assistant personnel, as women were not allowed to be members), a Cavalry Corps (which were really just riding clubs), and even their own courts. They were intentionally geared towards being an elite society within but apart-from the rest of Nazi Germany, one that would need as little contact as possible with outsiders. If a member of your family was in the SS, then you basically moved into a completely different social circle. One of Himmler's post-war goals was to turn Schleswig-Holstein into an SS nationstate.
When Germany was split after the war, East Germany got the Stasi (STAatsSIcherheitsdienst = State Security Service), practically a literal German translation of this trope's name, although the derivation runs the other way. They were able to field far more agents than the Gestapo ever could, (at their height, the Stasi had one agent for every 166 citizens, while the best the Gestapo could field was one agent for every 2000 citizens). An old saying in Germany goes, "The Gestapo were bone breakers. The Stasi were soul breakers."
The KGB had the Border Guards Chief Directorate, which consisted of 200,000 troops armed with its own tanks, aircraft, and ships. Although their chief task was sealing the border, not army action. Internal Troops, the Interior Ministry gendarmerie corps, would be closer, but they were glorified cops administratively, and thus had much less authority. In addition, the KGB had their own Spetsnaz and the Kremlin Guard Force.
Stalinist era NKVD/NKGB/MGB was more in line with this trope, as it was more extensive, and its troops fought directly in the Great Patriotic War.
In fact, NKVD troops are the direct ancestors of the current Internal Troops, as when NKVD was split into KGB and MVD in the postwar restructuring and post-Stalin power struggle, they went to the cops. The security half of the organization managed to keep the border police, though.
Belarus still maintains its own branch of the KGB even to this day.
South Africa: During the apartheid period, the South African Police was established to retain the National Party's white-minority rule over the black-majority population. When it didn't solve crime like a normal national police organization, it often inflicted crime — acts of brutal repression, torture, and state-sanctioned terrorism — on black dissidents. At one point, the SAP even ran a death squad that essentially carried out hits for the apartheid government against members of the African National Congress, both domestically and overseas.
North Korea: Ever since the economy began to fall apart in the early 1990's, the KPA has shown signs of this. Black markets have appeared that are run solely by the army and navy. Also, the secret police agencies are involved in black market activities such as the printing of superdollars.
The KPA's Guard Command is this, being one of two units responsible for protecting North Korean/foreign VIPs. According to Joseph Bermudez, the GC has tank units included to quell potential coup attempts.
Iran's Army of the Guardians of the Islamic Revolution, better known as the Islamic Revolutionary Guards Corps (IRGC) or just the Revolutionary Guards. They have their own Navy, Air Force, and ground forces, separate from the regular Iranian military. They also control the Iranian rocket forces and military-oriented nuclear research, meaning that should Iran get nuclear weapons, they would presumably all be under IRGC control. Also part of the IRGC is the Quds Force, which provides covert aid to foreign Islamic extremist movements. They also control the Basij, a paramilitary organization consisting chiefly of fanatical thugs, whose responsibilities consist of enforcing religious law (keeping women in headscarves, breaking up mixed-sex parties, keeping unrelated men and women separate, etc.) (sometimes violently), breaking up protests (usually violently), and generally intimidating people (how you can do that without at least the threat of violence in these circumstances is somewhat unclear to us). The IRGC has various other, more subtle secret-police like duties as well, but Iran being Iran, we don't really know too much about it.
To illustrate the Guards' position, back during the Iran/Iraq war they were recruiting school kids to the regular army with the express aim of 'being martyred' as cannon fodder. The Revolutionary Guards took advantage of this, but themselves employed things like tactics, and did not die in droves.
The Cardinal's Guards (well-known from The Three Musketeers) were actually such an organization. The guardsmen of Cardinal Richelieu were Musketeers. One company of Musketeers was assigned to the King, and one was assigned to the Cardinal. While there was no doubt some mild rivalry between the two companies, they were ultimately part of the same organization.
Rome had the Praetorian Guard — trope namers in their own right - a military force separate from the regular Roman legions that was charged with protecting the Emperor and other important Roman officials. They were heavily involved in politics and on more than one occasion chose who got to be Emperor of Rome (by killing them, such as Caligula, in some cases).
It should be noted that the Praetorians, if not outright stating it, may well have been the ultimate example for "Loyalty to the throne first, to the man who sits on it second", or if you want to be cynical about it, the epithet can be reworded to "Loyalty to the paycheque first, the man who signs it second" You could insult the senators, piss off the generals, whip the public into a furor. But the one thing all (remotely sane) Roman Emperors took care to avoid was making the Praetorians think that an assassination that would cause mass social upheaval would be the Lesser of Two Evils compared to letting you keep your job/life, and above all else, do not withhold a Praetorian's pay.
The Byzantines took this a step further with the Varangian Guard: they only hired foreigners to serve in the guard, as they knew foreigners were the only ones who wouldn’t have vested interests in the famously tangled politics of the Byzantine court, and would be less likely than the regular army to have qualms about slaughtering Byzantine Greeks if ordered to do so. “Varangian” is the Byzantine term for Germanic foreigners, particularly from Scandinavia: yeah, not only an State Sec and a Praetorian Guard, but one composed mostly of Vikings.There are possibly ways to make that idea cooler, but short of riding Bearsit's hard to think of them.
One of the scarier early examples of the trope was the Oprichnina of Ivan the Terrible. It was a semi-monastic fraternal order that was created to terrorize and depower the Boyar nobles who schemed against the Tsar. Its operatives wore black robes, rode horses with symbolic brooms and dog heads attached to saddles, and were formed into paramilitary terror squads that wiped out both manor homes and peasant villages. Aside from these operatives, the Oprichnina also owned vast tracts of land, had merchants working to finance it, and generally was a state within a state. By the end of the Oprichnina, Ivan's enemies were gone, but so was a large chunk of Russia's population. Some people think that the Oprichniks were the source of inspiration for Stalin's NKVD (Ivan the Terrible was Uncle Joe's favorite historical character).
The RomanianState Sec, Securitatea, was probably among the most brutal paramilitary societies ever. One could expect them knocking at/down the door of one's home and taking one and one's family to be beaten/shot for something like a half-finished Ceauşescu joke heard by one of the neighbors.
Turkey during the political instability of the 1970s did not have an actual State Sec (Secret Police is another question though). However, almost every political party that vied for supremacy had a paramilitary wing to conduct their morally dubious operations. More often than not, when the Government, the Army or the National Intelligence Agency needed its dirty work done, it would use one of these organisations. The most notorious and only surviving example is the nationalist Grey Wolves who have been involved with some of the blackest of government and army operations. These days, they're on the news regarding their part in a suspected military coup.
Armed political parties are a recurring theme in the Middle East. The kindling for Lebanon's Civil War was that every political force had a paramilitary organization, making it easy for the Arab-Israeli Conflict to light the fire; Hamas and Fatah's armed forces allowed them to fight a rather embarrassing civil war in 2006-7, and Hamas uses its armed wing as a secret police in Gaza; and any political party worth its salt had a militia under the Egyptian monarchy (before the July Revolution of 1952).
During the Saddam regime, there was a powerful security apparatus set up, but not quite formally unified as other examples. One part was the Iraqi Special Security Organization, which included the Special Republican Guard. It other branches included presidential bodyguards, "security" that monitored Republican Guard loyalty, communications, internal affairs, surveillance, administration, and even a "science" division - which only tested Saddam's food. The Republican Guard was another part of this informal StateSec, serving as a Presidential Guard and didn't fall under the Ministry of Defense. In addition, Saddam also had a separate irregular paramilitary branch loyal to him.
A strange case would be the various incarnations of the secret police under the Austrian Habsburgs, at least in their later days. Tracing their origins to Prince Metternich, the State Sec provided an unnervingly amiable (and deceptively incompetent) face, preferring to pull strings or subtly ease potential malcontents out of relevance rather than making them "disappear." Of course, this doesn't include an intricate spy network that not only stretched across the Empire but even beyond. Or the fact that it's helped Austria-Hungary to a degree shape their society as they see fit. Even as their actual competence decayed, the fact that elements of that system survived into the 1920s (after the end of World War I destroyed the monarchy)says a lot.
The United States Coast Guard is a military organization, but in peacetime it operates independently of the normal military. Today it's run by the Department of Homeland Security, but in years past it has been in the Department of Transportation and the Department of the Treasury(who also controls the Secret Service). Unlike most Real Life examples though, this one isn't evil, just unusual.
Fascist Italy had the 'Milizia Volontaria per la Sicurezza Nazionale' (Voluntary Militia for National Security), better known as 'Blackshirts', whose job was to keep the regular armed forces and the people in line. The Blackshirts are notable not only for being the direct model of the SS, but also for being more loyal to the state than the regime, best shown when Mussolini was deposed in 1943 and their only reaction was to replace the fasces buttons on their uniforms with star buttons like the regular armed forces as ordered by the new prime minister. Not to be confused with the trope, though many Blackshirts might have indeed been black shirts, and the trope was named after them.
The Milizia worked closely with the OVRA (Organizzazione per la Vigilanza e la Repressione dell'Antifascismo, 'Organization for Vigilance and Repression of Anti-Fascism'), a proper and frightenly efficient political police absorbed in the proper state police after the war. Or not: there is no actual evidence than the OVRA actually existed as nothing more than a way to scare opposers into submission and bait attention away from the police (that would do all the job) with a backronym that Mussolini (a former journalist) would have chosen purely because it sounded similar to 'piovra', the Italian name for 'octopus'.
Even peaceful and democratic Norway had shades of this. A unit called Statspoliti (there is something familiar about that name) operated in The Twenties and early into The Great Depression. They became historically known for repressing strikes and generally working for the government (and possibly the factory owners) against the labor unions. As such, they became increasingly unpopular, and may have contributed to making the Labor Party even more popular than they intended.
Then, the Labor Party itself invented a new security agency, surveilling communists for years after the war...