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.

Tabletop Games

 * Warhammer 40 K: 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 are led by their Skink priests, who interpret the wills of their gods.
 * The Theocracy of the Pale in the Greyhawk setting for Dungeons and 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'.