Wow, my first post has already got a comment. Its the big one, of course, Romans 13, the mainstay of Constantinian Christianity. I will write a quick answer now, and more when time allows. Thanks, "me", for the interest.
Romans 13 must be understood in light of Romans 12. We are simply commanded not to be overcome by evil, but to overcome evil with good. This includes how we confront the powers that be. We do not resist them by military rebellion. Bringing them down is God's job and as he ordains them to judge the wicked, he'll do that when he's ready. Rulers serve at an entirely different altar, that of vengeance, while we have been given the ministry of reconciliation. Christian anarchism seeks to disengage from entanglement with these institutions and offer an alternative society, based upon the mercy we have received rather than the penalty reserved for the wicked.