Ugh, everyone in this thread seems to not realize that the political spectrum is non-linear; the terms "left" and "right" are only one dimension of this concept. Imagine for a moment a Cartesian grid where the -x axis represents left-wing policy and the +x represents right-wing policy. On this grid, the +y axis would represent strong centralized government while the -y axis would represent no centralized government.
On both ends of the political spectrum (left and right), there are philosophies that advocate both strong centralized government and no central government. For example, on the extreme left both Communism and Anarchism advocate philosophies whereby people rule themselves. On the extreme right, you have philosophies such as Objectivism and Libertarianism which also similarly advocate for a decentralized or non-existent government, but do so with the intent of turning the world into one where only the fittest and most intelligent survive. They differ solely in their ideals of what they posit would happen in the absence of government; generally, left-wingers believe that everyone will hold hands and cooperate to make society as a whole better while right-wingers believe that everyone will tear each others' throats out whilst raping each others' daughters.
By contrast, both the left and right have ideologies advocating strong centralized government. On the extreme left you have Fascism, which is about as centralized a government as one can get. A less extreme left ideology would be Socialism which does not have the hallmark authoritarian control of Fascism but does place a lot of power in the central governing body. On the right, there are two forms of governance which are functionally identical to Fascism and Socialism. For Socialism, there is the hard paternalist state/police state (the latter being the more pejorative term) which resembles Socialism to a T minus the happy, fuzzy idealism. For Fascism, you have a monarchy/religious state which is again, functionally similar to Fascism except they force women to stay in the kitchen and make sandwiches.