I have no problem with the Ten Commandments in and of themselves. Actually, I think that if everybody followed them, this world would be a much better place. However, while one can even say that our current laws are based on the Commandments, calling them "The Ten Commandments" and carving them in stone the way these are places them in the Judeo-Christian mode of belief, therefore making them a religious object. Objects of religious significance do not belong in front of state courthouses.
Why not put the Ten Commandments in a museum or a park instead? That way, everyone will be able to see them, and it won't appear that the state is sanctioning one religion over another.
A note on the separation of church and state: Several people (read: religious right-wingers) have stated that the separation of church and state is not in the Constitution. This is not correct. Not only is freedom of religion explicitly stated, but the Constitution also says that the government should not include that which has caused strife and war in Europe for hundreds of years. What does this refer to? Religion, of course! Think of the Spanish Inquisition. Think of the Crusades. Think of the Thirty Years' War. You see what I mean?