Let everyone be subject to the governing authorities, for there is no authority except that which God has established. The authorities that exist have been established by God. Consequently, whoever rebels against the authority is rebelling against what God has instituted, and those who do so will bring judgment on themselves. For rulers hold no terror for those who do right, but for those who do wrong. Do you want to be free from fear of the one in authority? Then do what is right and you will be commended. For the one in authority is God’s servant for your good. But if you do wrong, be afraid, for rulers do not bear the sword for no reason. They are God’s servants, agents of wrath to bring punishment on the wrongdoer. Therefore, it is necessary to submit to the authorities, not only because of possible punishment but also as a matter of conscience.
This is also why you pay taxes, for the authorities are God’s servants, who give their full time to governing. Give to everyone what you owe them: If you owe taxes, pay taxes; if revenue, then revenue; if respect, then respect; if honor, then honor.
In studying this passage, I have consulted several commentaries, and I really appreciate what Doug Moo has written about this passage: "In demanding 'submission' to the state, Paul is not necessarily demanding obedience to every mandate of the state. Key to this restriction is the recognition that the word 'submit' (hypotasso) in Paul is not a simple equivalent to 'obey' (hypakouo)...[S]ubmission is broader and more basic than obedience. To submit is to recognize one's subordinate place in a hierarchy established by God. It is to acknowledge that certain institutions or people have been placed over us and have the right to our respect and deference. In addition to rulers (see also Titus 3:1), Paul also calls on believers to submit to their spiritual leaders (1 Cor. 16:16) and even to one another (Eph. 5:21-6:9)...one person is to recognize the rightful leadership role that another human being has in his or her life...[I]t seems to me, we can also, as believers, continue to submit to governing authorities even as, in certain specific instances, we find that we cannot obey them. When they order us to do something incompatible with our allegiance to God, our higher authority, we must, as Peter and John put it, 'obey God rather than men' (Acts 5:29)."
Dr. Moo then goes on to add: "One final word on this issue, however, must respect the intention of this passage. Clearly, it does not intend to encourage disobedience. It warns us agains the danger of ignoring the rightful place government has in God's ordering of the world according to his purposes. Government--and each individual state and ruler--is appointed by God. Christians seeking to do God's will, therefore, recognize the right of the governing authorities to command them to do things, and they should, as much as possible, do what the government says."
And finally: "The debate will no doubt continue; what will be be important is that believers seek to establish what they believe on the basis of all Scripture, not just isolated texts (emphasis mine)."