For the USA, the central bank is the Federal Reserve System.
In a few cases, the central bank is private, and otherwise similar to a regular commercial bank. In other cases, it is directly controlled by the head of government. In most cases, however, it is a government agency that is shielded from direct control.
OTHER IMPORTANT CENTRAL BANKS
European Union--European Central Bank (ECB).
Japan--Bank of Japan
China--People's Bank of China
United Kingdom--Bank of England
See also the International Monetary Fund and the Bank for International Settlements.
The BIS acts as a bank to most of the world's central banks.