I know some people who are will have a separate computer for all of their online banking and bill paying. They don't use this computer to browse the web, check their email, get on Facebook or anything except paying their bills.
When it comes to using your computer and security, I don't think you can be too careful. I know that I am much more conscious of it than I used to be.
All it takes is for one person to get your information and your life can become a mess in a hurry. Making sure your computer is secure and taking the necessary precautions is pretty important for anyone who spends time online.