I use a netbank service - it gives me access to my accounts and all my banking needs. I even have a savings account which is ONLY an electronic account. No keycard and no physical access to it whatsoever.
Before logging on, i ensure a secure connection was established. I Trust my browser as i keep my computer clean and protected - And i change my password as needed.
The biggest vulnerability in your details being stolen is accessing your banking from multiple different computers, as opposed to the single 1 computer you have at home/office.