From my article on the subject:

Anarcho-Capitalism: Anarcho-capitalists believe that governments monopolize services that would be better left to corporations, and should be abolished entirely in favor of a system in which corporations provide services we associate with the government. The popular sci-fi novel Jennifer Government describes a system that is very close to anarcho-capitalist.

Civil Libertarianism: Civil libertarians believe that the government should not pass laws that restrict, oppress, or selectively fail to protect people in their day-to-day lives. Their position can best be summed up by Justice Oliver Wendell Holmes' statement that "a man's right to swing his fist ends where my nose begins." In the United States, the American Civil Liberties Union represents the interests of civil libertarians. Civil libertarians may or may not also be fiscal libertarians.

Classical Liberalism: Classical liberals agree with the words of the Declaration of Independence: That all people have basic human rights, and that the sole legitimate function of government is to protect those rights. Most of the Founding Fathers, and most of the European philosophers who influenced them, were classical liberals.

Fiscal Libertarianism: Fiscal libertarians (also referred to as laissez-faire capitalists) believe in free trade, low (or nonexistent) taxes, and minimal (or nonexistent) corporate regulation. Most traditional Republicans are moderate fiscal libertarians.

Geolibertarianism: Geolibertarians (also called "one-taxers") are fiscal libertarians who believe that land can never be owned, but may be rented. They generally propose the abolition of all income and sales taxes in favor of a single land rental tax, with the revenue used to support collective interests (such as military defense) as determined through a democratic process.

Libertarian Socialism: Libertarian socialists agree with anarcho-capitalists that government is a monopoly and should be abolished, but they believe that nations should be ruled instead by work-share cooperatives or labor unions instead of corporations. The philosopher Noam Chomsky is the best known American libertarian socialist.

Minarchism: Like anarcho-capitalists and libertarian socialists, minarchists believe that most functions currently served by the government should be served by smaller, non-government groups--but they believe that a government is still needed to serve a few collective needs, such as military defense.

Neolibertarianism: Neolibertarians are fiscal libertarians who support a strong military, and believe that the U.S. government should use that military to overthrow dangerous and oppressive regimes. It is their emphasis on military intervention that distinguishes them from paleolibertarians (see below), and gives them reason to make common cause with neoconservatives.

Objectivism: The Objectivist movement was founded by the Russian-American novelist Ayn Rand (1905-1982), author of Atlas Shrugged and The Fountainhead, who incorporated fiscal libertarianism into a broader philosophy emphasizing rugged individualism and what she called "the virtue of selfishness."

Paleolibertarianism: Paleolibertarians differ from neolibertarians (see above) in that they are isolationists who do not believe that the United States should become entangled in international affairs. They also tend to be suspicious of international coalitions such as the United Nations, liberal immigration policies, and other potential threats to cultural stability.