It depends on what you are protecting. If it is personally sensitive info, credit card info or similar them you must protect it appropriately. Storing passwords in the clear would not be appropriate in these cases!
Credit card protection requirements are global (PCI-DSS), data protection laws exist in Europe, USA and other regions eg DPA 1998 in UK. In the US, Gramm-Leach-Bliley Act protects personal financial information; Fair Credit Reporting Act protects credit history information; Health Insurance Portability and Accountability Act protects health information.
Also, have a read of Thomas Pornin's blog post on this - Why passwords should be hashed - this will give a greater insight.