There seem to be ways to open a bank account as a non-US resident. Services related to this might be an opportunity, like middleman shipping services. I've been told you can open a Bank of America account online/over the phone without a SSN if you can use someone's US address.
I read, but haven't verified, that one can open an ING US account if you have an ING account in your country.
I had no difficulty at all opening an account with Harris Bank. It's possible that it helped that I'm Canadian and they're owned by a Canadian bank, though.
I read, but haven't verified, that one can open an ING US account if you have an ING account in your country.