Here is a list of 45+ forms of government to get your creative juices flowing for your fictional societies. Have fun and play safe!! Remember: this is not an inclusive list. There are many government types and sub-sects that have multiple "pure" ideologies as well as some that I have not listed. I suggest your local library and the Internet as valuable resources if you want to examine any of these in more depth.
(The definitions presented here are as they were presented to me. I make no claim on their validity and neither condone nor condemn any specific form of government for the purpose of this article.)
Anarchy -- No rulership or enforced authority
Aristocracy -- Rule by the most prominent citizens ("rule of the best")
Bureaucracy -- Rule through heads of various departments and conducted by their chief administrators
Communist state -- Single-party rule or dominant-party rule of a communist party and a professed allegiance to a communist ideology as the guiding principle of the state
Confederation -- An association of sovereign member states, that by treaty have delegated certain of their competences to common institutions
Consociationalism -- Guaranteed group representation, often viewed as synonymous with power-sharing
Corporatism -- Economic, political, or social organisation that views a community as a body based upon functional distinction and roles amongst individuals
Demarchy -- Governed by randomly selected decision makers who have been selected by sortition (lot)
Democracy -- Derived from the people, either by direct referendum (direct democracy) or by means of elected representatives of the people (representative democracy)
Despotism -- Single entity rules with absolute and unlimited power, and may be expressed by an individual as an autocracy or through a group as an oligarchy
Dictatorship -- Autocratic form of government in which the government is ruled by an individual, the dictator
Ethnic democracy -- Combines a structured ethnic dominance with democratic, political and civil rights for all
Ethnocracy -- Representatives of a particular ethnic group hold a number of government posts disproportionately large to the percentage of the total population that the particular ethnic group(s) represents
Exilarchy -- Established and constituted for rule over an ethnic or religious diaspora rather than over the place of origin whence the diaspora originates
Fascism -- Organize according to corporatist perspectives, values, and systems, including the political system and the economy - often strongly right-wing
Federation -- A union of partially self-governing states or regions united by a central (federal) government
Feodality -- Feudal natured government where each successive layer of authority derives power and authority from the one above and pledges fealty likewise
Feudalism -- Political and military system between a feudal aristocracy (a lord), and his vassals
Gerontocracy/Geriatocracy -- Rule by leaders who are significantly older than most of the adult population (elders)
Gynarchy -- Rule by a only women or a ruling class that passes through the women
Kleptocracy -- Government that takes advantage of governmental corruption to extend the personal wealth and political power of government officials and the ruling class ("rule by thieves")
Kratocracy -- Government by those who are strong enough to seize power through force or cunning
Kritocracy / Kritarchy -- Rule by judges
Magocracy -- Rule by magi, wizards, or witches
Matriarchy -- Rule by the eldest females
Meritocracy -- Organization wherein appointments are made and responsibilities assigned to individuals based upon demonstrated intelligence and ability (merit), evaluated using (frequent) institutionalised examination
Militocracy -- Headed by the military leaders and the armed forces in general
Monarchy -- All political power is absolutely or nominally lodged with an individual or individuals (king, duke, etc). As a political entity, the monarch is the head of state, generally until their death or abdication, and "is wholly set apart from all other members of the state
Noocracy/Pedocracy -- Rule by the wise and learned
Ochlocracy/Mobocracy -- Government by mob or a mass of people, or the intimidation of constitutional authorities
Oligarchy -- Power effectively rests with a small segment of society distinguished by royalty, wealth, family ties, military control, or religious hegemony
Panarchism -- Political philosophy emphasizing each individual's right to freely join and leave the jurisdiction of any governments they choose, without being forced to move from their current locale
Parliamentary -- System of government in which the ministers of the executive branch are drawn from the legislature and are accountable to that body, such that the executive and legislative branches are intertwined
Plutocracy -- Rule by the wealthy, or power provided by wealth
Presidential -- An executive branch exists and presides (hence the name) separately from the legislature, to which it is not accountable and which cannot, in normal circumstances, dismiss it
Puppet state -- Nominal sovereignty controlled effectively by a foreign power
Republic -- At least a part of its people have some element of formal control over its government, and in which the head of state is not a monarch
Socialist state -- Nationalized economy, usually operated according to a plan of production, so that capitalism and the procurement of wage labor for private profit is abolished at least in the major productive and social spheres ("worker's state")
Sociocracy -- Consent-based decision making among equivalent individuals and an organizational structure based on the interdisciplinary study of structure of regulatory systems
Syndicracy -- A body of syndics, each representing some business interest
Technocracy -- Government in which engineers, scientists, and other technical experts are in control of decision making in their respective fields
Thalassocracy -- "rule of the sea" - Refers to a state with primarily maritime realms - an empire at sea
Theocracy -- Government in which a god or deity is recognized as the state's supreme civil ruler, or in a higher sense, a form of government in which a state is governed by immediate divine guidance or by officials who are regarded as divinely guided
Timocracy -- "1) A state where only property owners may participate in government
2) A government where rulers are selected and perpetuated based on the degree of honor they hold relative to others in their society, peer group, or class"
Tribal -- Social group existing before the development of, or outside of, states
Tyranny -- Rule by one who has taken power by his or her own means as opposed to hereditary or constitutional power
Union -- Sovereign state governed as one single unit in which the central government is supreme and any administrative divisions (subnational units) exercise only powers that the central government chooses to delegate
