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Dungeons & Dragons
In Dungeons & Dragons the two main types of magic are arcane magic and divine magic. A government headed by the disciples of divine magic is called a theocracy (due to such magic being derived directly from the setting's gods). In a magocracy, only those with skill and power in arcane magic (wizards learn arcane magic through study and practice, while sorcerers have the innate ability to use arcane magic) have a voice in government. Thus, power is limited to the few who have the education (and in such societies, wealth is often needed for an education), or magical heritage.
Typically, arcane magic users will have privileges, and the citizens will live in fear. Divine magic may be restricted, or limited to followers of the theocracy. In the world of Mystara, the Principalities of Glantri have banned all divine magic users.
In the Forgotten Realms campaign setting, the present-day nation of Thay is ruled by the Red Wizards. Past magocracies in the setting include Netheril (of which the City of Shade is a remnant) and Imaskar (a remnant of which retreated into the Underdark at the fall of the empire).