To be frank, this passage presents difficulties. It is (or certainly appears to be) political, and in a way that affirms the legitimacy of existing regimes. As one commentator puts it, "Romans 13 was Adolf Hitler's favorite Bible passage." After all, as Paul says, "there is no authority except from God, and those authorities that exist have been instituted by God."
Other commentators have argued (though not persuasively to my mind) that the authorities to whom Paul refers are not civil but church authorities. But the references to legal justice (and the sword of punishment) and to taxes could not possibly refer to the church.
So we are left with the plain statements of a man who also said the Jesus (NOT Caesar)is Lord. I don't think that Paul is contradicting himself here. Jesus remains in control of our lives in a way that the civil authority never can be, but the civil authority imposes order in a way that Jesus, at least in the current age, does not. This therefore becomes a compelling argument for the separation of Church and State; we pay tangible taxes to the earthly taxing body, which keeps civil order; but we remit our true selves to the divine order.
There is no earthly ruler that God has not allowed to take power. There have unquestionably been (and still are) monstrous tyrants and dangerous fools. I don't believe there is anything in Paul's words to contravene the statement that "whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new government." That is, and will remain, our story. But ultimately we still answer to the One Lord who created Heaven and Earth.