This, however, is from US tax law section 871 – Tax on non-resident aliens: http://www4.law.cornell.edu/uscode/uscode26/usc_sec_26_00000871—-000-.html

“(i) Tax not to apply to certain interest and dividends” … 2.A “Interest on deposits, if such interest is not effectively connected with the conduct of a trade or business within the United States.”

In summary – non-resident aliens can indeed open a bank account in the US and the bank interest isn’t taxable.

Actually foreign nationals can open bank accounts in the US, and there is indeed a special tax exemption for them for bank interest (see link below). I do know foreigners who have an account in the US. One of them actually visited the US; also got a special id number first – it looked like social security but clearly stated “Not authorized for employment”. She also included her parents – I don’t remember if they also visited or if they could do it by mail. At some point they needed to fill out additional forms with passport numbers, foreign address, purpose of the account. Their relative here has a power of attorney and the US relative’s address is listed as main mailing address.

As to taxes, there is a special tax exemption for interest on personal bank accounts for foreign nationals provided that the account is personal and not for trade or business. I actually helped to translate the form they needed to fill out, and it spelled the tax exemption quite clearly. I think at some point IRS wanted to take this exemption away, but the banks were afraid that they’ll lose all of these foreign deposits that help US economy.

You can read about the tax exemption here:
http://www.thetaxguy.com/return.htm – scroll to “Exempt interest”: “Interest paid on deposits with banks, on accounts or deposits with certain financial institutions, or on certain amounts held by insurance companies, are exempt from U.S. tax even though they are U.S. source income.” I had a more official link, but I can’t find it at the moment.

Out of curiosity I just googled to see if foreign nationals can open an account without coming to a US and found this: http://isolutions-ng.com/USbank.pdf — I haven’t read the article in detail but it lists banks that apparently can do it by mail with appropriate documentation.