Wherefore [ye] must needs be subject, not only for wrath, but also for conscience sake.
Note 8 at Ro 13:5: In Ro 13:1-4, Paul gave two reasons for being subject to civil government, which he summarized here. First, we need to be subject to it because the government has the power to punish us if we aren't. Second, since God has ordained government, we have to submit or our consciences will condemn us for violating the instruction of God.
Therefore, even if we could break the laws of government and get away with it, we shouldn't, because we are also violating God's Word. So laws that are not in direct opposition to God's Word should be kept, whether or not we will get caught and whether or not we think they are important.
In the next verse (Ro 13:6), Paul specifically mentioned taxes as one of those laws that we should comply with (see note 9 at Ro 13:6). This could be updated to include speed limits, local ordinances, and a host of other things that many of us may disagree with but cannot say are directly against God's Word. The government has a God-given right and responsibility to regulate and establish order, and we should comply for consciences' sake. Our submission to government and our submission to God are intertwined.