I found a website that teaches about Romans 13, correcting the popular misinterpretation that it teaches slavery (or mindless submission) to civil government. The buzz among many online personae these days definitely has been leaning toward mindless submission (foretaste of the Delusion to come?), even to an illegal and wayward government. In light of this, I've added the site to the Links section on the right for easy reference.
A couple of things are not phrased the way I would put it, but the site is very good nevertheless. For example, it says the U.S. was not founded on Christian principles. Technically, the author is correct; the U.S. was founded on the Constitution, a secular document. However, the mentality of the Constitution's authors was decidedly Christian and this mentality is necessary for a Textually Originalist interpretation. Nevertheless, his point is accurate enough. Take a look at the site. I think his treatment overall is quite good.
UPDATE: If you go to the parent site of this treatment of Romans 13, you'll quickly see an unusual mentality. The author speaks of our calling to be removed from the State system, being bound only to Heaven. In a sense, he's right, and I laud his efforts, even if they are somewhat misguided. Even as our spirits are reborn of God, our bodies are still trapped here in a fallen world. While we can deny our bodies for a short time (e.g., fasting)--in fact, we should do so--we cannot fully escape them. When we join our Lord in the Kingdom, we will receive new bodies, ones born sinless and not of the fallen world, but until then, we live straddling two worlds. In this way, and per the website's author's comments on 1 Peter 2:13-14, it is good that we are lawful in this world, but we do not serve man's government as if it were our master. We are lawful because such behavior is a testimony to God and of our submission to God Himself and His authority. We are not lawful because we submit to worldly government but because we submit to God. Again, we do not submit to worldly government; men are not our master, as God is our only Master. If we happen to observe man's law, it is because we obey the Lord, and man's law--in such coincidence--doesn't conflict. If we happen to defy man's law, it is because we obey the Lord, and man's law in this case does conflict. Our observance or defiance of man's laws, then, is all but happenstance, as our obedience belongs to the Lord alone.
Another perspective
Dr. Chuck Baldwin has written about Romans 13. You will find his views on this topic here. In Dr. Baldwin's view, the state does have some legitimate, God-given authority, but it rests entirely with the Constitution.
In my view, the positions of the Embassy of Heaven and of Dr. Baldwin are skewed, though I would align more closely with that of Dr. Baldwin. I believe that any authority held by civil government must rest entirely and explicitly on Scripture. To the extent that the Constitution does this, I can agree that civil authority, and the subsequent obedience of the believer to that authority, rests in it. However, I question whether the Constitution is entirely complicit with Scriptures. (That's actually a good topic for another discussion.)
The basis for my agreement has already been stated by Wayne. Civil authority is legitimate insofar as it aligns with Scripture. When it does so, we can and should submit to it -- but not for its own sake. Our only law is the law of God, and we submit to civil authority for the Lord's sake alone.