Wikipedia is so goddamned helpful and amazing:

Free banking is a theory of banking which invokes only market forces, with a conspicuous absence of central banks and any banking regulations, with only the general commercial laws applicable. Free banking includes no restrictions on the formation of banks, the issue of banknotes, the acceptance of demand and term deposits, and the provision of loans, advances and other forms of credit. Banks would also be free to engage in non-banking businesses such as insurance, and non-banks would be free to engage in the business of banking. Banks would set their own credit, capital and reserve policies.

… There is speculation that with electronic currencies free banking can evolve into Anonymous internet banking. The implications of this for the monetary system are unknown, and much of the rigorous theory in this area has been abandoned for a wait and see attitude.

Electronic money: “Electronic money (also known as electronic cash, electronic currency, digital money, digital cash or digital currency) refers to money or scrip which is exchanged only electronically. Typically, this involves use of computer networks, the internet and digital stored value systems.”

See also the Free Banking Era which lasted from 1837 to 1862, and ended because of the Civil War, interestingly enough (The War of Norther Aggression?). In the Free Banking Era, only state-chartered banks existed.

See also:

1. Wildcat Banking
2. National Banking Act of 1863, under which Lincoln issued greenbacks.
3. United States Greenback Party
4. United States Note
5. Legal Tender Act of 1862