As for my own campaigns, democracy, especially as classically practiced and understood, is never represented in the games I run.
The last D&D game I ran, the characters were part of a dying nomadic hunter-gatherer society living through an ice age. The bands were so small that they either were one or a collection of two or three matrilocal family groups; these extended households were managed by clan mothers (grandmothers). The bands practiced a form of radical exogamy whereby they could only sleep with someone of a different clan totem. This made interactions with other groups highly socially and culturally important but, due to the paucity of resources, such meetings were intense and of short duration.
The game I'm currently running (not D&D, my own personal BRP-D20 hybrid) is one of those epic campaigns ranging over an enormous geographic area. As a result, I have several forms of government represented:
The Empire of Laman is a pre-modern bureaucratic despotism with a large service-gentry bureaucracy closely managing a set of smaller political units it has recently absorbed -- kind of like a cross between Imperial China, the Inca Empire and the Spanish Empire under the Bourbons. The three main entities that wield political power in the empire are its military, its judges (the service gentry governors) and a high-profile religious secret society, the Gadiantons, (its members go about masked). The army and Gadiantons are of roughly equal power, and are sometimes the same people, especially at their high echelons and are both directly accountable to the emperor. The service gentry, as in most despotisms, is held firmly in check for fear of it becoming an incipient aristocracy.
The Seven Kingdoms are a weird hybrid political entity held together in a loose military confederacy and nominally ruled by a high king, Onondaga. However, the Onondaga only rules in times of peace. And in times of peace, the kingdom is so politically decentralized, he is, at most a mediator in disputes among its members. In times of war, the confederacy is ruled by a Dux Bellorum or War Chief who has sweeping power to declare martial law, levy troops and appropriate resources if the kingdoms are threatened. Under him are six enormous matrilocal tribes, comprising six of the kingdoms and the seventh, which is a former monarchy, a city-state now ruled by its former service gentry, a weak aristocracy that has devolved much of its powers to self-governing cults, ethnicities, neighbourhoods and other units sufficiently atomized as not to represent much of a threat. It is a miltiarily weak power that is, in the nicest possible sense, basically paying tribute to the six kingdoms that protect it.
The Petty Realms, which the characters haven't reached yet, will be like early European feudalism.
I'm sure I'll think of more but that's probably an okay start.
