"Give to Caesar what is Caesar's, and to God what is God's."
The interpretation I hear most often these days for this particular verse is that just as Caesar's image is imprinted on what you need to give, God's image is imprinted on all human beings. Thus, we are to give ourselves to God.
But I have other questions arise when I read this passage. Does Jesus mean that all money belongs to the government, so we should not expect such wealth to accumulate in the lives of His faithful followers? Another question that arises is what all belongs to God? Everything? I have argued for years now that care for the poor, handicapped, prisoners, and the like rests first and foremost with the church. This seems clear from the account just a few short chapters later, where what separated the sheep and the goats was what they did and didn't do. The indication seems clear to my reading that God has given ministering to the disadvantaged to the church to accomplish. It's not primarily the government's responsibility.
Are you giving to God what is truly due Him?