Be wary of JPMorgan Chase or Wells Fargo, and I'd outright recommend never banking with Bank of America. I've had business accounts over the years with all of them.
If you have a smaller, regional bank or credit union with good capital adequacy, little/no exposure to construction loans (the next "shoe to drop"), no exposure to sub-prime loans, and strong reserves, consider using them. You'll get better customer service. Just make sure the bank/credit union can provide all the services you need before moving your balances.
The big banks have dramatically raised fees, reduced customer service, and if you ever have a problem you're a nobody unless you have a $100M account.