Three free, easy options (but of course not perfect) to hopefully feel and be a little more secure with online banking, ranked from least inconvenient to most inconvenient.
Least Inconvenient: Use
Trusteer Rapport in your browser and set it up to protect your login credentials at sensitive websites. Once you've set it up to protect certain sites, you just surf as normal. Of course, some malware have been created to disable Rapport specifically, so you're hopeful that Trusteer keeps up with such attacks, and you keep up with the updates.
Middle Inconvenient, but possibly more secure: Set up an encrypted virtual machine dedicated for banking use. Plain Jane is better than full of features so you're not tempted to do anything but your banking business while logged in to it. I think a good option might be
Lubuntu with
Virtual Box. Once it's set up, you just have to have the discipline to wait a minute for the Guest OS to start up before you do your online banking.
Most inconvenient, but likely the most secure: Use a live CD that doesn't connect to your hard drive at all. Such as
Lightweight Portable Security, which was created by the Dept of Defense to make their own telecommuting more secure, but is available for public download. But you'll have to wait for your computer to restart with the live CD before you do your online banking. And if you have an iMac with wireless keyboard, you'll have to wait ten minutes for it to go to sleep before you can wake it up and use the keyboard. Helpful hint: A live DVD should boot more quickly than a live CD. And if you save any PDF statements from your bank's website, you'll need to use a USB drive.