The Many Mandates of the Fed
The Federal Reserve Act states the objectives of monetary policy: “The Board of Governors of the Federal Reserve System and the Federal Open Market Committee shall maintain long run growth of the monetary and credit aggregates commensurate with the economy’s long run potential to increase production, so as to promote effectively the goals of  maximum employment,  stable prices, and  moderate long-term interest rates.” (numbers in [brackets] added)
If you have difficulty reconciling this sentence with textbook macroeconomics you are not alone. There is no obvious definition of maximum employment (zero unemployment?) or stable prices (zero inflation?) or moderate long-term interest rates, but in any case the Fed must do all three simultaneously. Even if we do not precisely understand the Fed’s official instructions from Congress, we can see that they are fairly broad; a Fed chairman can always claim that a particularly policy was aimed at one of the objectives.
In contrast, other Central Banks whose have a single objective to maintain price stability (for example the ECB, see here) and attach secondary importance to employment and growth. There are a number of other jobs for the Fed described in the Federal Reserve Act but they are of lesser importance.
Congress created the Fed and holds a good deal of power over it. The Humphrey-Hawkins legislation (see section 108 of the rather large pdf) required the Fed to report to Congress twice a year about how it is meeting its objectives; while the legislation expired in 2000, the Fed chairman voluntarily testifies before Congress twice a year (more often if there are important issues) and is required to answer a number of questions on various issues.
If Congress is not happy with the Fed’s performance they could theoretically redesign the system and replace the Fed with something else. While it would take a major crisis to provoke such a reaction, this scenario happened during the Great Depression. In 1942, Congress took interest rate policy away from the Fed and gave it to the Treasury Department (see here); the Fed only regained its independence in 1951.
So the Fed is very responsive to Congress. The Fed Chairman routinely endures lengthy questioning from Congress about many topics in an effort to be responsive to the concerns of Congress (a search on youtube.com for Fed Chairman Bernanke produces over 1000 videos, many of which appear to involve Congressional testimony), and tries to carefully explain policy to preserve the Fed’s independence in the future.
The Fed chairman technically has two separate appointments: a term as governor (just like that of the other six governors) that lasts 14 years (unless the chairman initially takes the remainder of the term of another governor) and a four-year term as chairman (see here for Chairman Bernanke’s terms). Again, the chairman can remain chairman until a new chairman is nominated. The practical result is that Fed chairmen in recent years have worked closely with each new President; Chairman Greenspan was nominated initially by President Reagan and then renominated by Presidents Bush and Clinton. The current understanding in Washington appears to be that markets would be upset by the ouster of a Fed chairman who is doing well, making administrations reluctant to change. Chairman Bernanke’s handling of the current economic mess will likely determine whether he will be renominated when his term as Chairman expires in January 2010.
There is one important mandate that the Fed does not have: managing the external value of the Dollar. It is a curious relic of the 1951 Fed-Treasury accord that the Treasury is responsible for the Dollar, so that only the Secretary of the Treasury will speak about the Dollar’s value or order intervention in currency markets (which will be carried out by the Fed). Most economists believe that the value of the Dollar is largely determined by monetary policy, which is planned and executed by the Fed. But for legal/political reasons, the official authority is in the Treasury.