for he is God's servant for your good. But if you do wrong, be afraid, for he does not bear the sword in vain. For he is the servant of God, an avenger who carries out God's wrath on the wrongdoer. (ESV)
Paul makes a statement in the beginning of this verse that might have been hard for the people in first century Rome to accept. When he says, "He is God's servant for your good," he is referring to the government official who is meting out justice. Rome was filled with corruption. They were not a "Christian" government. How could Paul say that Rome was God's servant?
There is a generalization here for all followers of Jesus Christ to understand. The general role of governments are to promote the health, safety and prosperity of their citizens. Does this always happen effectively? Of course not. Should we live our lives in opposition to the government over us? Of course not.
If we do wrong we can expect judgment to be carried out by the government whose laws we have violated. In some respect, the ungodly government is an unwitting agent of God's wrath. God is the ultimate sovereign authority. He will bring out his wrath by using the local established human governments.
Paul, as an Apostle, used his Roman citizenship when it would benefit the reputation of the church. If you read through the book of Acts you will discover that one of the purposes of Luke's narrative account of the early Church is to show that they were not an anti-government bunch of radicals, but rather humble servants of Jesus Christ who honored God and honored the king.
Walk humbly with others on this earth. The government, for the most part, is not your enemy. God can even use an ungodly government to mete out judgment and wrath.