I used to write authentication systems for Visa and can confirm that everything Ajayre wrote is correct about the encryption applied by https and the weaknesses related to encrypted passwords.
Not that my opinion is so valuable, but he or she went to so much trouble to type it that at least I can back them up.
Personally, I would never, ever, ever give my banking password to anyone . If someone says they need that to provide me a service, I don't need that service. I'm fairly certain the advice from banks is the same. Anyone thinking of doing this should talk to your bank.
