Brother Will says: There are two ways to interpret this verse:
1. Everything belongs to God, so nothing belongs to Caesar. If everything belongs to God, who should the wealth go to instead of Caesar? To God's children, the poor who will inherit the earth.
2. Pay the taxes that are required by good governments. How do you recognize good governments? They do God's work: they feed the hungry, heal the sick, free the prisoners, and help the poor inherit the earth.
The first argument is the anarchist's, and the second is the socialist's. I like both, but I think the second's more practical. Which Jesus had in mind, no one can guess. My belief is we have free will so we can work out the details ourselves.
Recommended: Render unto Caesar... - Wikipedia, which includes this:
Mennonite pastor John K. Stoner spoke for those who interpret the parable as permitting or even encouraging tax resistance: “We are war tax resisters because we have discovered some doubt as to what belongs to Caesar and what belongs to God, and have decided to give the benefit of the doubt to God.”