OBEDIENCE TO GOD VS OBEDIENCE TO GOVERNMENT
Should we obey the government? What if the laws of government conflict with the laws of God? Yes, this is the conflict of God vs government.
Obey the Government...
Let every soul be subject unto the higher powers. For there is no power but of God: the powers that be are ordained of God. Whosoever therefore resisteth the power, resisteth the ordinance of God: and they that resist shall receive to themselves damnation. For rulers are not a terror to good works, but to the evil. Wilt thou then not be afraid of the power? do that which is good, and thou shalt have praise of the same: For he is the minister of God to thee for good. But if thou do that which is evil, be afraid; for he beareth not the sword in vain: for he is the minister of God, a revenger to execute wrath upon him that doeth evil. Wherefore ye must needs be subject, not only for wrath, but also for conscience sake. For this cause pay ye tribute also: for they are God's ministers, attending continually upon this very thing. Render therefore to all their dues: tribute to whom tribute is due; custom to whom custom; fear to whom fear; honour to whom honour. (Romans 13:1-7)
Submit yourselves to every ordinance of man for the Lord's sake: whether it be to the king, as supreme; Or unto governors, as unto them that are sent by him for the punishment of evildoers, and for the praise of them that do well. For so is the will of God, that with well doing ye may put to silence the ignorance of foolish men: As free, and not using your liberty for a cloke of maliciousness, but as the servants of God. Honour all men. Love the brotherhood. Fear God. Honour the king. (2 Peter 2:13-17)
Then said Pilate unto them, Take ye him, and judge him according to your law. The Jews therefore said unto him, It is not lawful for us to put any man to death: (John 18:31)
...Except when That Means Disobeying God
And believers were the more added to the Lord, multitudes both of men and women.) Insomuch that they brought forth the sick into the streets, and laid them on beds and couches, that at the least the shadow of Peter passing by might overshadow some of them. There came also a multitude out of the cities round about unto Jerusalem, bringing sick folks, and them which were vexed with unclean spirits: and they were healed every one. Then the high priest rose up, and all they that were with him, (which is the sect of the Sadducees,) and were filled with indignation, And laid their hands on the apostles, and put them in the common prison. But the angel of the Lord by night opened the prison doors, and brought them forth, and said, Go, stand and speak in the temple to the people all the words of this life. And when they heard that, they entered into the temple early in the morning, and taught. But the high priest came, and they that were with him, and called the council together, and all the senate of the children of Israel, and sent to the prison to have them brought. But when the officers came, and found them not in the prison, they returned, and told, Saying, The prison truly found we shut with all safety, and the keepers standing without before the doors: but when we had opened, we found no man within. Now when the high priest and the captain of the temple and the chief priests heard these things, they doubted of them whereunto this would grow. Then came one and told them, saying, Behold, the men whom ye put in prison are standing in the temple, and teaching the people. Then went the captain with the officers, and brought them without violence: for they feared the people, lest they should have been stoned. And when they had brought them, they set them before the council: and the high priest asked them, Saying, Did not we straitly command you that ye should not teach in this name? and, behold, ye have filled Jerusalem with your doctrine, and intend to bring this man's blood upon us. Then Peter and the other apostles answered and said, We ought to obey God rather than men. (Acts 5:14-29)
God Vs Government
What Scripture states in these passages is that our first priority is to obey God's laws. In areas where Scripture is silent, we are to obey the laws of government. For example, speeding is a sin; although Scripture is silent on speed limits, laws of government are not. However, it would be different if the government passes laws against witnessing (in some countries, they have). In this case, as Scripture commands us to witness, Scripture also calls us to break such a law. We can certainly also fight to change a law like that (see the page on politics).
 All scripture references are from the King James Version unless otherwise noted. Please see my about page for why I chose this translation.