Switzerland is one such example, where the law only permits an bank account to be associated with an individual in cases of severe criminal acts or atrocities, such as identifying a terrorist's bank account. Otherwise, the details of the account holders are held securely, the account is only identified by a number, and a bank employee violating privacy is punished quite severely by law. Costa Rica and the Bahamas also have attractive banking laws.
There are a number of reasons to use anonymous banking:
Anonymous banking is sometimes considered one of the main aspects of Private Banking.
The USA Patriot Act has created many new rules for U.S. Banks in an attempt to defeat Anonymous banks. A list of such banks or shell banks are given to the U.S. banks who are not allowed to wire money to them. All new customers to a bank must now be asked if they are a U.S. citizen, and if not, if they are a foreign political figure or related to one in any way. They must also give their occupation and state if they expect foreign money to be wired to them. The main goal is not as much to combat terrorism as to stop corrupt foreign politicians from being able to successfully drain their countries treasuries.