A friend of mine got a phone call today; it was someone trying to sell him a membership for product discounts. It was supposed to include free frequent flier miles and a $100 gas card. The woman on the phone asked for his bank account number so that they could verify that he had the money to spend on the membership. My friend did the smart thing and hung up immediately.
NEVER EVER EVER give someone your bank account information over the phone. Even if your bank calls you, they should not ask you about your account information; they have it all right there. They might ask you for the last 4 of your Social Insecurity number or you mother's maiden name. They should never ask for the whole thing though. If they get insistent about something, tell them you will go to a branch to take care of it. They'll likely hang up on you.
You can find more information about identity theft HERE