Anarcho-Socialist - (traditional Anarchism) - The belief that all forms of power are ultimately corrupt. Often, "Socialism without the State". Some Greens and some Socialists.
Social Democratic - (British Labour, modern day Scandanavia, Ralph Nader, et.al.) - The belief that social justice is best facilitated by democratic control of most, if not all, social institutions. Some Democrats and most Greens.
Socialist - (Marx, Engels, Fourier, St. Simon) - The belief that political equality, and social justice, are impossible without economic equality. Some Greens and most Socialists.
Anarcho-Capitalist (Rand/Rothbard/David Friedman) - The belief that eventually, the state will be rendered unnecessary by the market. Some Libertarians.
Libertarian (American Anti-Federalists, Thomas Paine, Boaz, Murray, Milton Friedman) - The belief that the size and scope of government should be minimized as far as possible. The Libertarian Party and some Republicans.
Liberal - (Locke, Adam Smith, Madison, J.S. Mill, both Roosevelts) - The belief that social justice is best facilitated by limited, popular government and free (and fair) markets. Some Republicans, most Democrats, most Reformers.
Communist - (Lenin, Castro, Mao) - The belief in a state that controls all aspects of economic life, even at the expense of political liberty. Arguably "state capitalism," as compared to anarcho-socialism.
Conservative - ("The Moral Majority", et. al.) - The belief that the state exists to maintain the status quo, politcally and economically. Some Republicans and some Reformers (like Buchanan).