The US Federal Reserve is not a government agency...
edit: To clarify, the presidentially-appointed Board of Governors of the Federal Reserve are considered a government agency, but they are only a part of the Federal Reserve. There's also the FOMC, some regional Federal Reserve banks, and some private banks as well (but they are required to subscribe to non-transferrable stock in the regional Federal Reserve banks).
Although I'm sure I don't need to tell Flip this.
I think there are problems with Central Banking Systems like this (as does Ron Paul, who is a member of the House Subcommitte on Domestic Monetary Policy). He would know better than I. Most notably, I think they haven't always been responsible with control of inflation....but that's a very mixed bag.