i opened mine with Bank of Oklahoma (america) roughly 2 years ago. I did use my passport as one of the two ID's required, so that goes with what Sparky said. I have no fees on my account whatsoever (free personal checking account), and got a free debit card (visa). Only costs i'll get is when i order checks, but i haven't done so yet. Also, i can use my debit card as a credit card in european stores and i'm not getting charged any extra fees - NONE whatseover.
More recently, though, my brother opened an account with the same bank just last month. He also just showed his passport & US issued drivers license.