country. If you plan to have a merchant account (for example to accept credit card payments online), not being a US person your only solution might be to open a merchant account with a bank or financial institution in your country, in which case you would need to have a bank account in your country anyway.
Keep in mind, in order to open a bank account for a US company in your country the company documents need to be certified through a process called "Apostille/Embassy Certification" (see below).
Alternative #2: Bank Account in Another Country
You might as well opt for opening a bank account in an offshore jurisdiction. Many jurisdictions are known for their beneficial environment for business activity and make it easy to open bank accounts remotely, so you might want to consider researching this option further.
Alternative #3: PayPal and Similar Services
Depending on your business needs you might want to opt for using financial services such as PayPal. If you are having hard time opening bank account and merchant account for your business, using PayPal or similar services (such as Google Wallet, Amazon Payments, etc.) to collect payments from your client might be your only (but nevertheless viable) option.
Alternative #4: 2Checkout, Stripe & Skrill (ex-MoneyBookers)
If the only reason why you need a U.S. bank account is to be able to collect payments from your U.S. clients you should consider using 2Checkout, Stripe, or Skrill for credit card processing. 2Checkout, Stripe and Skrill allow merchants based in a number of countries covering wide range of industries to collect online payments from buyers across the globe.
Alternative #5: High-Risk Merchant Accounts
If your country or industry is not covered by 2Checkout or Skrill there is an option of high-risk merchant accounts. The terms of use for those accounts usually include higher that regular fees (between 7% and 15%), and also longer payout delays (2-3 weeks, compared to 2-3 days for regular accounts). Some other terms might apply. When you establish some history with the high risk merchant account provider (such as 6-9 months of flawless processing) you could qualify for better terms. Also, your processing history with one provider could be used in the future to apply for a merchant account with another provider, with better terms.
When opening a bank account in the US a company representative appearing in person in the bank would need to bring specific company and personal documents. Below you can see the list of all possible documents a representative would be required to have in his/her possession: