I tried Ally. They said I could sign up, no money down and send a check later. Did that. I was waiting for my welcome package and a bank card so I could withdraw cash at a bank machine. The Friday befoe a long weekend I got an e-mail "I you don't make a deposit in the next 48 hours we're closing your account".
Well, first I needed a bank account to send them a check. If I transferred my pension over to them as I had intended, I would have had no bank card and no checks until the got off their butts and sent me a welcome package via snail mail.
So, for now I'll stick with Chase, but I hear good things about HSBC,