Oh, the paranoia. A good attitude to have, actually.
Online banking is a necessity for many people. I don't have the time to waste going to the local branch and standing in line to transfer money between accounts, pay bills, etc.. Time is money.
You're more likely to have someone steal your CC numbers when you use the card at the mall than online.
Online banking is as safe as you make it. Period. Most banks (all banks in Canada, by federal law) protect your money and guarantee that protection. If your money gets ripped off, they replace it. Just like Visa.
First, find out what your bank's policy is regarding identity theft, compromised accounts and online banking. This is assuming you didn't do that before opening an account with the bank. If they don't satisfy your needs, find another bank.
Next, harden your link to the bank. I have two PCs in my house that are hardwired to my firewall and those are the only PCs that are used for banking. I've gone so far as to block access to the bank sites from my netbook and notebook so I don't get lazy. Wireless encryption is not foolproof.
Finally, check your bank's encryption. Mine uses a 128-bit RSA encryption scheme that is, for all intents and purposes, safe. If yours uses anything less .. find a new bank.