When banking online, always use strong passwords (See, How do I choose a good password?) and do not use this password for any other purpose. Check to be sure that your bank uses high-end encryption (See, Does your bank use high-end encryption?).
One important way that you can increase your security when banking online is to take advantage if your bank offers digital security device. This adds “something you have” during logins or transactions. This is much more secure because even if someone steals your user ID and PIN they cannot steal your account or money without the device. This device might be a token you use to generate a unique one-time-password (OTP) that is different for every login. You can also use it to approve every important transaction with a unique “digital signature.” Since the device is not even connected to the PC, it is safely out of the reach of hackers.
Many banks today offer this extra layer of security, including Barclays PINsentry or Bank of America’s SafePass. Often, the service is optional and not widely advertised, so ask your bank if they offer the option to use a digital security device to log on to online banking services.