There is a large movement in the United States to put the Ten Commandments everywhere. Supporters want them in the public schools, in government buildings at the local, state and federal levels, and they probably would like to get them on money, but there are space concerns so there isn't much lip service paid to that.
As you might have guessed, I say nay. And that is probably what the Supreme Court would say if the matter ever gets that far (it has in the past, but for some reason the issue keeps coming up). The Supreme Court will allow it, but only in the context of other historical documents relating to law.
All that is good in theory, but the Ten Commandments is a religious document, no bones about it. There were written laws around before the Ten Commandments detailing the same laws, and to call it the basis for our legal system is a gross misrepresentation.
Why? Because only three out of ten Commandments are actually illegal: Killing, stealing, and lying (under very specific circumstances)--the rest relate to religious fidelity and religious morals. Lying is the Commandment most frequently broken in modern society, and is usually not illegal, so really only 2.5 Commandments are illegal (in fairness, the translation "bear false witness" is an accurate representation of its legal equivalent).
There is absolutely nothing illegal about worshiping an idol, or hating your parents, or coveting the neighbor's daughter until you need a cold shower. Nothing at all. I can work all day on Sunday, Saturday, or Friday, the Sabbath days for Christianity, Judaism, and Islam, respectively.
Public religious display, even by majority rule, is wrong. There is no logical reason for venerating the Ten Commandments in this way. I suppose if a majority of the citizens advocated "Divine Guidelines for Living" then that would be acceptable. No such thing exists, but say it did, and looked like this: