One verse that sprang immediately to my mind was 1 Peter2:16. To provide a context for the verse, I'll start with vs.13:
"Submit yourselves for the Lord's sake to every human institution, whether to a king as the one in authority, or to governors as sent by him for the punishment of evildoers and the praise of those who do right. For such is the will of God that by doing right you may silence the ignorance of foolish men. Act as free men [and women], and do not use your freedom as a covering for evil, but use it as bondslaves of God. Honor all people, love the brotherhood, fear God, honor the king. Slaves, in reverent fear of God submit yourselves to your masters, not only to those who are good and considerate, but also to those who are harsh. For it is commendable if someone bears up under the pain of unjust suffering because they are conscious of God. But how is it to your credit if you receive a beating for doing wrong and endure it? But if you suffer for doing good and you endure it, this is commendable before God. To this you were called, because Christ suffered for you, leaving you an example, that you should follow in his steps" (1 Peter 2:13-21 NIV).
What strikes me in this passage is that Christians are free. Ironically, however, we express our freedom as slaves to God! When we submit to and honor the "powers that be" we are fleshing out our obedience to God, who alone is the One with ultimate power and authority in all the universe.
Notice that Peter was quick to qualify the Christian's freedom. Never are we to use our freedom in Christ as an excuse or cloak for doing something evil. Christians are not to be antinomianists who flaunt the law, whether man's or God's. God, after all, expects His children to fulfill His law's demands as they are led by the Holy Spirit (see Romans 8:4). While we are perhaps wise to abandon the old adage "Let your conscience be your guide," Christians in particular are to have enlightened, sensitive consciences to which they are to listen.
Having said that, however, just as there are always going to be controversial, "grey areas" of behavior within a given community of Christians today (as there was in the first century with the issue of meat sacrificed to idols--see Romans 8:1-9:15 and 1 Corinthians 9), so also will there be differences of opinion among well-meaning Christians as to whose conscience is correct and whose is not, as well as which secular laws and regulations must be obeyed and which may or must not be obeyed.
Clearly an edict from a government or repressive regime making it illegal to preach the gospel is something we cannot obey in good conscience. Other laws will not be so clear-cut, however, as the ban on preaching Christ crucified. (Having said this, I assume the better part of wisdom in countries where "proselytizing" is banned is to limit preaching, teaching, and sharing one's faith either to underground, home churches, or to clandestine gatherings of people, generally, whether in remote locations or any other non-public places. The same would apply, I feel, to bans on disseminating the written word of God, in any medium. Years ago an uncle of mine frequently smuggled Bibles into countries where Bibles were prohibited. Today, an organized effort among Christians in repressive countries to transmit Scripture via email, podcasts, Twitter, or carrier pigeons would be, I believe, sanctioned by God.)
In other less-obvious ways, we must not be dogmatic. For example, to one Christian the seemingly insignificant act of putting money into an expired parking meter as a "random act of kindness" is clearly wrong (particularly if there is a local ordinance making the act a misdemeanor!), whereas to another Christian, it is quite permissible. In such situations, I suggest each Christian must listen to his or her conscience. If the latter believer is doing the good deed deliberately to flaunt the law, then perhaps s/he should re-examine his or her motives! If the former, seemingly "overly sensitive" believer does not feed the meter, does that therefore mean the latter Christian is right and the former, wrong? No, before God each one is right.
In conclusion, when God's word is clear about a given action's rightness or wrongness, and the powers that be agree with God's word, Christians have an obligation before God both to obey and not to disobey. In the few cases in which to obey the government would be to disobey God, we should listen to our enlightened consciences, which are to be informed by God's word, and we should also seek advice from and follow the example of the Christian leaders among us, whether godly elders, deacons, pastors, ministers, priests, mentors, and so on.
If you feel I should bolster my answer with more concrete examples, do let me know and I'll try to come up with a few more. Don