Depends on the bank you work with.
For my professional needs I have a bank in Luxembourg, the BCEE. The BCEE never sends me mail, I have a mail icon on my screen when I connect to my account via their secure website (secured by the traditional login name + password and a one time token) if a message is waiting for me.
To make any important change to my account, I have to physically present myself in one of the many branches, justify my identity and then ask for what I need.
I very much doubt that any criminal is going to be able to modify anything remotely.
Of course, if you live in the USA, things are very much different.
Biting the hand that feeds IT
