Just wanted to pass on my experience on Monday with opening an account through Barclays. I went in with a copy of my lease but was told they don't accept that as documentation. I braced myself to hear that there was no way I could open an account, but ended up being very surprised when I was told I could open an account with just my passport and my US driver's license! It was incredibly simple--I was told the catch is that the US address on the license needs to be your last US address and within 3 months of living there. I was also told that they prefer a US utility bill or bank statement to a US license, but it wasn't a problem that I didn't have these statements on me (though I suppose this could depend on which location you go into, etc). After they took all my information and ran a credit check, I was told that I qualified for all but their most exclusive accounts, though I would not be able to get overdraft protection on any account just yet.
The banker who opened my account advised me to come back within about 4 or 5 months to see about applying for a credit card and overdraft protection.