The way I have always viewed the political spectrum, from grad school days, is with the free republican form of government in the middle of the spectrum - the "ideal balance" if you will of personal freedom, social and personal responsibility, with a representative form of governance balanced by diffusion and absolute checks on power. This middle is what was envisioned by the American Founders (but never perfectly realized of course, like all ideals). I always saw this as the middle. Not very different than what Luis (and others here) said in a different way.
As you moved leftward, you arrived at the welfare state (soft socialism) and then to true socialism...pressing eventually to the extreme of totalitarian communism. As you moved rightward you would come to crony capitalism, old style Monarchy in its various forms (all the way to its harshest form as seen in the Empire of Japan that mixed Monarchy with fascism) including feudalism, to ecumenical or religious-based governing structures and finally to the harshest mixture of these totalitarian forms: fascism. The irony of the spectrum of course is that it seemed to bend into a circle, as hard communism and fascism are nearly indistinguishable to the common man. This worked and was rather elegant - and explained the 20th century beautifully.
However, I never viewed the spectrum as absolute, encompassing all possible forms of human civilization...in one sense libertarianism is a mixture of left and right that arrives oddly enough not at the middle seemingly any time...and the modern Greens seem to arrive at both extreme fascism and/or communism on business regulation while keeping touch with soft socialism on other social issues. And then there are the Anarchists - who are just into destruction ala Clockwork Orange - they revel in the law of the jungle. They are the devil's antithesis to the idea of structure and are always outside any spectrum of governance.
