Guys, read the chapter in full: This verse is not about separation of church and state. It was about blasphemy.

What was going on in this scene is that the Pharisees were trying to trick Jesus into saying something treasonous, so they could report him to the Roman government and have him executed (which is later exactly what happened, although not because of this particular scene by itself).

If you go back a few verses to Mark 12:13, it says explicitly that they were trying to trick him into saying something he wasn't supposed to say.

In this chapter, the Pharisees tried to trick Jesus by asking him if it is proper for a Jew, who is prohibited from paying tribute to the Roman gods (or any other gods besides Yahweh) because of the First Commandment, to still pay taxes to the Roman government - more specifically to Caesar, who was considered by the Romans to be a form of god-on-earth.

In 1st-century Galilee, there was something of a gentlemen's agreement between the Jews and the Roman government that the Jews would be allowed to have their own temples and worship their own gods (which was technically illegal under Roman blasphemy laws), as long as they still paid the Roman taxes and pretty much stayed out of the Romans' way.

If Jesus had said "no" as far as paying these taxes, this would have been treason, and he would have been arrested by the Romans and executed then and there, instead of later in the story.

But he knew the Pharisees were not asking out of honest curiosity about his teachings (it says so explicitly in Mark 12:15), but rather just trying to get him in trouble, so instead, he said: "Why are you trying to trick me? Bring me a Roman coin and let me look at it." And he shows them the picture of Caeser's face on the coin and says, "Give back to Caesar what is Caeser's, and give to God what is God's."

What this means in the context is, these coins are earthly things with no real value - give them back to the Romans, where they came from in the first place. What God wants from us is not these Roman-issued coins; rather, our lives belong to God, and so we are supposed to give them to God, by following his laws, as given to Moses in the Old Testament. So yes, don't argue about paying these taxes, pay them - it doesn't matter anyway - and follow Jewish law, because that is what God wants Jews to do.