Plato in his book The Republic (375 BC) divided governments into five basic types (four being existing forms and one being Plato's ideal form, which exists "only in speech"):
Aristocracy (rule by law and order, like ideal traditional "benevolent" kingdoms that are not tyrannical)
Timocracy (rule by honor and duty, like a "benevolent" military; Sparta as an example)
Oligarchy (rule by wealth and market-based-ethics, like a laissez-faire capitalist state)
Democracy (rule by pure liberty and equality, like a free citizen)
Tyranny (rule by fear, like a despot)
These five regimes progressively degenerate starting with aristocracy at the top and tyranny at the bottom.
In his Politics, Aristotle elaborates on Plato's five regimes discussing them in relation to the government of one, of the few, and of the many. From this follows the classification of forms of government according to which people have the authority to rule: either one person (an autocracy, such as monarchy), a select group of people (an aristocracy), or the people as a whole (a democracy, such as a republic).
Thomas Hobbes stated on their classification:
The difference of Commonwealths consisteth in the difference of the sovereign, or the person representative of all and every one of the multitude. And because the sovereignty is either in one man, or in an assembly of more than one; and into that assembly either every man hath right to enter, or not everyone, but certain men distinguished from the rest; it is manifest there can be but three kinds of Commonwealth. For the representative must need to be one man or more; and if more, then it is the assembly of all, or but of a part. When the representative is one man, then is the Commonwealth a monarchy; when an assembly of all that will come together, then it is a democracy or popular Commonwealth; when an assembly of a part only, then it is called an aristocracy. In other kinds of Commonwealth there can be none: for either one, or more, or all, must have the sovereign power (which I have shown to be indivisible) entire.