I am a pretty paranoid backup person. I am a software and web developer and run the finances as well as software development for my own compay. So I have a lot of very vital data on my computers.
I don't use the web I as I have just too much material to easily back up this way and, frankly, I don't really trust it (large amounts of company sensitive data). I currently have three main backup hard drives. One is backed up daily, another weekly and the third monthly. On top of that I have another drive kept in a different location, which I swap out with one of the others periodically (maybe four times a year).
This has saved my skin several times. I travel around on business a fair bit and my laptop can take quite a hammering. Over the years I would estimate that each laptop I have owned has had maybe 3 hard drive failures in the space of around 5 years each (about how long I keep a laptop before getting a new one). Desktop or Tower machines have failed less often but have still failed.
And don't forget to keep a check on your backup drives themselves - they can and do fail as well!