"What Is Free Banking, and Why Should I Care?"

Learn Liberty: What would happen if we didn't have a central bank? Prof. Lawrence H. White explains that private banks would be able to circulate money by issuing notes and checks redeemable for coin. Trustworthy banks would make arrangements to accept each other's notes and checks. Banks would have better incentives than the federal government to ensure their currency retained its value, because if it didn't, people would bank elsewhere. By contrast, central banks controlled by the government are able to devalue currency as they see fit and can even quit redeeming notes for coins of real value if they want to do so.
It sounds like social-science fiction, but there are numerous real-world examples in history of successful free-banking systems. In fact, central banks arose largely because governments wanted an institution willing and able to lend them money with easy terms, not because of any problem with the free-banking system. Free markets offer the most efficient system for allocating goods and services, and money is no exception. As failures among central banking systems mount, it is time to reconsider the alternative of free banking. Source