There's something exotic and kind of exciting about having a Swiss bank account; you don't even have to be Swiss to have one.

It is possible to open an account, even for people in the US.  American citizens that work for Swiss companies who end up stationed in the country for an extended period of time are the most likely to open and maintain an account, but really anyone can do it.  To open an account at a Swiss bank, you'll need the following:

• You don't have to, but it's a lot easier to go to Switzerland and open an account in person 
• Demonstrated that you're at least eighteen years of age
• If you're not Swiss, you'll need a valid passport
• You'll need some kind of documentation to prove where your money originates
• You'll need verification of your address
• The Swiss need some proof of the origin of the funds you wish to deposit
• You'll also have to identify beneficiaries of the funds 

It does sound complicated, but Swiss bankers can't accept funds from criminal activities.  Swiss banks are known for secrecy.  It's a criminal act in Switzerland, punishable by prison, for a banker to reveal any details about his or her clients.  However, there's also an agreement between Switzerland and the US that Swiss banks will report earnings generate to the IRS.  There are certain circumstances in which this requirement doesn't apply, but for most people, there's just no getting around it. 

So, yes, it is possible to open a bank account in Switzerland.  The allure is still there, but most of the reasons why people want such an account no longer apply!