The Theocracy

Simply put, a Theocracy is any society in which the The Church is the government. Often the laws of a theocracy are based off religious law, or claims that God (or Gods) is the supreme ruler of their state. This is especially prevalent in pre-modern settings.

It's common to have an official state religion, but this doesn't necessarily equate to a theocracy or even an especially religious country. For example, in England the head of state (the monarch) is also the head of the Church, bringing an overtly religious aspect into the governmental system, but England and the UK in terms of population are much less religious than nearby, officially secular Ireland and France.

Note that true theocracies, where secular government is virtually non-existent, are fairly rare. Most often the Church will simply have a lot of secular power and sometimes a parallel government: authority over religious/moral laws, it's own bureaucracy, it's own army, etc.

Compare Church Militant, where the clergy is Badass, but not necessarily the rulers of a country. A Corrupt Church is often the head of a Theocracy, but not always.

Comic Books

 * In the DC Comics miniseries World of Krypton it's shown how the government of Krypton came to be science based. There were three competing factions: one for science, one for democracy, and one for a Theocracy. They decided to let the Kryptonian gods decide. One representative from each faction went out into a thunderstorm with a rod; whichever one didn't get hit by a bolt would be the chosen. Science won after theocracy and democracy's reps each got hit. In The Stinger of the story the scientist admitted to a time-travelling Kal-El that he had used a non-ferrous metal in making his rod. He didn't consider it cheating since the gods told him to do so - or so he claimed.

Literature

 * The Lands of Holy Order in Hard to Be A God.
 * In The Chosen by Chaim Potek, Rebbe Malter is both hereditary Rabbi and clan chief of the local community of immigrant Russian Hassidics in New York. Truth in television, as noted in Real Life.

Tabletop Games

 * Warhammer 40,000: The ginormous Imperium of Man is very much a theocracy, given that they have a Physical God as its former leader. However, ever since a prominent Ecclesiarchy member went mad and tried to form his own Imperium within the Imperium, the Ecclesiarchy is no longer allowed to keep "men under arms". Hence the Sisters of Battle. Also, their priests accompany the Imperial Guard into battle wielding inspiring speeches and eight-foot-long chainswords.
 * Similarly, on the Chaos side the leaders tend to be those who the gods most favor. However, they aren't really priests, as the Chaos gods would much rather their followers kill loyalists and aliens instead of holding masses.
 * The Lizardmen of Warhammer Fantasy Battle are led by their Skink priests, who interpret the wills of their gods.
 * The Theocracy of the Pale in the Greyhawk setting for Dungeons & Dragons. In the Living Greyhawk campaign, the real-world region assigned to it was Utah.
 * Jarzon in Blue Rose.

Web Comics

 * In The Order of the Stick Azure City is technically this. It's ruled by Lord Shojo, who is also the leader of the Sapphire Guard, an order of Paladins; he argues that this means his secular jurisdiction isn't limited because nor is their gods'.

Real Life

 * For many centuries the synagogue was the Jewish community center in a number of cities, with business and legal matters as well as strictly religious matters being conducted there. For instance when a Jew left on a journey he was required to announce it at the synagogue to give anyone who he owed money to allow time to make a claim. In some countries (like the Ottoman Empire) the rabbinical "government" answered for its congregation to a gentile prince as if it was a feudal vassal. To some degree this continues today and some Hasidim even have their local security known as "Shomrim."
 * Similarly in Venice (despite the city being stereotyped for the impious traits of avarice and lust), the main focus of many people's political identity was the semi-autonomous church parish. This was more a matter of practicality as a parish easily doubles as a city ward.
 * A number of Medieval bishoprics possessed fiefs and armed forces of their own, including the Papacy. In Italy there was often uncomfortable ambiguity between the Pope's position as Pope and his position as "King of Rome." Today, it endures in the form of Vatican City, which is located within Rome itself.
 * Two examples of this ambiguity are the War of the Sicilian Vespers and the War of the League of Cambrai where the Pope attempted unsuccessfully to weaponize excommunications and interdicts as a psy ops against Aragon and Venice respectively.
 * The Holy Roman Empire had a number of "Prince-Bishops" who at least nominally answered to the Kaiser, among the most notable being those of Salzburg and Cologne. This isn't even getting to the political and sovereign power The Teutonic Knights wielded in Prussia and the Baltic.
 * To a large degree the Church was a willy-nilly theocracy in the West. As the only large and experienced bureaucracy that could carry on Roman administrative traditions it processed red tape for a society composed of warlords and patriarchs evolving into kings and elders evolving into parliaments. As time went on it became part of a tripartite medieval division of power into the landed warriors, the Church, and the Commercial classes.
 * The position of Caliph (defunct since the fall of the Ottoman Empire but carrying a memory in much of the Islamic world), meant "chief teacher and high king."
 * The Byzantine Empire became a very peculiar example of this trope over generations. Even compared to the Medieval Papal States, the separation of Church and State in Constantinople was so blurred that the Emperor at times clashed with the Patriarch over religious authority.
 * Utah's history bears some shades of this, thanks in part to its origins as a Mormon Cult Colony before becoming part of the United States. Although the last trappings of theocracy were abolished before the end of the 19th Century, the LDS Church still wields indirect influence in the state government.
 * The modern State of Israel is an aversion. It was defined as a refuge for Jews and gives them an advantage both in immigration and the making of the Constitution. As well as in local customs down to ration packages in the IDF. What it does not do is define what a Jew is supposed to believe, nor restrict citizenship to Jews and indeed the most religious of Jews have always given it no more then ambiguous favor on the whole.
 * A more sinister version then all of these was the Arrow-cross Party which ruled in Hungary for a short time. It had a weird combination of Catholic supremicism (to the point where it would have embarrassed most Catholics including The Pope)and romanticism for the Pagan Magyars(hence the arrow cross logo in representation of the National Weapon of steppe nomads). The Arrow Cross was known for bloodthirsty anti-Semitism and though little remembered may have taken such things farther then any European faction except the Nazis themselves.
 * In point of fact, the Arrow-Cross was probably closer to the sci-fi stereotype of this then any other version, which usually consists in real life of something like a Medieval Kingdom with different titles.
 * Depending on how hard you wish to push the analogy, a typical revolutionary state bears resemblance to this, indeed perhaps closer to how we imagine "theocracy" then less eccentric examples from traditional religions. The Party stands in place of the clergy, the party doctrine is the dogma, and the state is it's cat's paw(the boss of course often using all of them as puppets).
 * Any nation where the ruler is seen to be a living god, such as Pharaohnic Egypt.