Mozy is the online backup service that I hear the most about. It's at mozy.com.
I have never used it or any online backup service. You have to come to a conclusion about how you feel with all of your personal data sitting up there in the sky somewhere, the expense, and the longevity of the company you are dealing with. They all use high levels of encryption, but I remain uncomfortable with the general idea of my data being passed off like that.
The alternatives are doing your own backups locally--to DVD, to external drives, to internal drives, or to USB sticks. Use multiple methods and keep one copy off-site--like in a safe deposit box--to guard against theft, fire, disaster.
As a general proposition, I avoid Norton, but I have no clue about this particular product.