Every other agency has a department or branch of government between them and the Congress/Administration.
A number of independent agencies exist.
In terms of domestic policy, probably the most important today is the Federal Reserve System which has the responsibility to conduct the nation's monetary policy, supervise and regulate banking institutions, maintain the stability of the financial system and provide financial services to depository institutions, the U.S. government, and foreign official institutions.
The first was the Interstate Commerce Commission (ICC) was a regulatory body in the United States created by the Interstate Commerce Act of 1887, which was signed into law by President Grover Cleveland. (The agency was abolished in 1995.) The ICC's original purpose was to regulate railroads (and later trucking) to ensure fair rates, to eliminate rate discrimination, and to regulate other aspects of common carriers.
Wikipedia lists about 30 examples
under an article entitled Independent agencies of the United States government
An example that many of us remember was when in 1971 Congress eliminated the Cabinet position of Postmaster General and created the United States Postal Service, defined by statute as an "independent establishment" of the federal government.