I have been using this online backup service at mozy.com. It actually works really well, doesn't get in the way, and you can restore files from the web.

If you use this link, then I get an extra 512MB quota also. (he he)

The system is free, and you start with 1GB. Paid subscriptions are available if you need more space. The client tool that does the backups is available for Windows only (as far as I know).