United States Banking began in 1781 with an act of United States Congress that established the Bank of North America in Philadelphia. During the American Revolutionary War, the Bank of North America was given a monopoly on currency; prior to this time, private banks printed their own bank notes, backed by deposits of gold and/or silver.
Robert Morris, the first Superintendent of Finance appointed under the Articles of Confederation, proposed the Bank of North America as a commercial bank that would act as fiscal agent for the government. The monopoly was seen as necessary because previous attempts to finance the Revolutionary War with paper currency had failed; after the war, a number of banks were chartered by the states under the Articles of Confederation, including the Bank of New York and the Bank of Massachusetts, both of which were chartered in 1784.
The Bank of North America was succeeded by the First Bank of the United States, which the United States Congress chartered in 1791 under Article One, Section 8 of the United States Constitution, after the Constitution replaced the Articles of Confederation as the foundation of American government. However, Congress failed to renew the charter for the Bank of the United States, which expired in 1811. Similarly, the Second Bank of the United States was chartered in 1816 and shuttered in 1836.

The era of free banking
In 1863, Congress passed the National Bank Act in an attempt to retire the greenbacks that it had issued to finance the North's effort in the American Civil War. This opened up an option for chartering banks nationally. As an additional incentive for banks to submit to Federal supervision, in 1865 Congress began taxing any issue of state bank notes (also called "bills of credit" or "scrip") a standard rate of 10%, which encouraged many state banks to become national ones. This tax also gave rise to another response by state banks -- the invention of the demand deposit account, also known as a checking account. By the 1880s, deposit accounts had changed the primary source of revenue for many banks. The result of these events is what is known as the "dual banking system."
The dual system of banking has survived to this day. New banks may choose either state or national charters (a bank also can convert its charter from one to the other). Until 1989, banks with national charters (national banks) were required to participate in the FDIC, while State Banks either were required to obtain FDIC insurance by state law or they could voluntarily join it (usually in an attempt to bolster their appearance of solvency). After enactment of the Federal Deposit Insurance Corporation Improvement Act of 1989 ("FDICIA"), all commercial banks that accepted deposits were required to obtain FDIC insurance and to have a primary federal regulator (the Fed for state banks that are members of the Federal Reserve System, and the FDIC for "nonmembers").

The dual banking system
The Federal Reserve Act of 1913 established the present day Federal Reserve System and brought all banks in the United States under the authority of the federal government, creating the twelve regional Federal Reserve Banks which are supervised by the Federal Reserve Board. Notwithstanding the Glass-Steagall Act of 1932 and the Banking Acts of 1933 and 1935, which were attempts to reform various banking abuses, the Federal Reserve System has remained more or less unchanged through to the present day. The Glass-Steagall Act was repealed in 1999, whereas the Banking Act of 1933 simply strengthened the supervisory powers of federal authorities and created the Federal Deposit Insurance Corporation.

The Federal Reserve System
Legislation passed by the federal government during the 1980s, such as the Depository Institutions Deregulation and Monetary Control Act of 1980 and the Garn-St. Germaine Depository Institutions Act of 1982, diminished the distinctions between banks and other financial institutions in the United States. This legislation is frequently referred to as "deregulation," and it is often blamed for the failure of over 500 savings and loan associations between 1980 and 1988, and the subsequent failure of the Federal Savings and Loan Insurance Corporation (FSLIC) whose obligations were assumed by the FDIC in 1989. However, some critics of this viewpoint, particularly libertarians, have pointed out that the federal government's attempts at deregulation granted easy credit to federally insured financial institutions, encouraging them to overextend themselves and (thus) fail.

Deregulation
Some brands in the banking/financial services industry today are the result of a merger where the acquiring bank assumed the brand name of the bank it took over. This happened in the case of these mergers:

The Nations Bank/BankAmerica merger
The Norwest/Wells Fargo merger
The Firststar/US Bank merger
The Travelers/Citibank merger
The Chemical Bank/Chase merger
The Travelers Group/Citicorp merger
First Union/Wachovia merger
J.P. Morgan Chase/Bank One merger Top three changes in banking profitability

Bank size information
Figures as of September 30, 2006, in U.S. dollars.
U.S. Bancorp — 217 billion
Countrywide Financial Corp. — 193 billion Top ten bank holding companies in the U.S. ranked by assets
As of June 30, 2005 in U.S. dollars. These are U.S. deposits only. This is not a ranking of the largest U.S.-based global banks.

Bank of America Corp. — 577 billion
J.P. Morgan Chase & Co. — 384 billion
Wachovia Corp. — 284 billion
Wells Fargo & Co. — 256 billion
Washington Mutual Inc. — 186 billion
Citibank — 131 billion
U.S. Bancorp, Inc. — 117 billion
SunTrust Banks — 106 billion
HSBC Bank USA NA — 62 billion
World Savings Bank — 58 billion See also

History of Money and Banking in the United States by Murray N. Rothbard. Full text (510 pages) in pdf format
Rothbard, Murray N. / Richardson & Snyder. 1983. The Mystery of Banking Full 177-page text in pdf format.