I initiated a wire transfer today, and at one point one of the credit unions involved in the transfer called me up to verify some things before they made the transfer.
When she asked for my account passcode, I froze, and asked to call her back. She understood completely. I called her back, and finished the transaction.
It surprised me a little bit that they (the credit union) could call me up and ask for my account information like this. Certainly with e-mail they and most other businesses go to great lengths to say that they will never ask for your password by e-mail.
I don't doubt that my credit union acted properly, but are they in general allowed to conduct business this way, or are there restrictions?

