13Then they sent to Him some of the Pharisees and the Herodians, to catch Him in His words. 14When they had come, they said to Him, "Teacher, we know that You are true, and care about no one; for You do not regard the person of men, but teach the way of God in truth. Is it lawful to pay taxes to Caesar, or not? 15Shall we pay, or shall we not pay?"
But He, knowing their hypocrisy, said to them, "Why do you test Me? Bring Me a denarius that I may see it." 16So they brought it.
And He said to them, "Whose image and inscription is this?" They said to Him, "Caesar's."
17And Jesus answered and said to them, "Render to Caesar the things that are Caesar's, and to God the things that are God's."
And they marveled at Him.
I don't know a lot about the Pharisees, but it seems like they were often testing Jesus, especially about the law. In Mark 10:2, they tested him by asking if it lawful for a man to divorce his wife. It makes me wonder if they were sticklers for the law.
It says they marveled at Him. They had been trying to trip Him up with one of the more difficult questions of the time, and Jesus easily defined the separation of church and state. Rather than them showing Jesus up, they probably learned something that day.
I think this question was not so much just about taxes, but more the role of Caesar to the citizens. Caesar wished to be treated as a god. I think the collection of taxes was one form that Caesar expected of the citizens to give of themselves to him, to demonstrate their loyalty to him. I think that here Jesus is saying to give the coins to Caesar that are expected of them, but worship only God.
As we go through life, we are to be good citizens of whatever we belong to (country, job, social groups, etc.). Being a Christian does not exempt us from obligations to these other organizations to which we belong, in fact I think being a Christian holds us to a higher standard of meeting commitments. We are to uphold those obligations as long as we are not giving to the organization those things which belong to God.
We live in a totally different time. Paying taxes to our country does not seem to be a very difficult question. There are many other questions regarding church and state that are not as clear cut as to what our obligations are compared to what belongs to God, such as fighting for your country, school prayer, etc. We do not always have the image on the object to tell us if it belongs to God or to country, but Jesus' statement still holds true. Give to your country that which belongs to your country, but give to God that which belongs to God.