The most valuable thing on your computer is probably your data. You may well back it up to DVD or another hard drive but a fire or theft could leave you in the ****.
There are a number of services that automatically back up your data over the net for free (you need broadband for this really).
The one I have experience of is Mozy. You get up to 2GB of storage for free. This is plenty for all my emails and office docs. Photos, MP3s etc. will quickly take you over this limit however but you can upgrade to more space for a fee. However having your documents backed up for free can't be bad.
Mozy installs as a service on your computer and every so often (approx every 2 hours) finds any documents in your backup set that have changed or been created and backs them up over your broadband link. Documents are encrypted and there are throttling options and "don't back up unless idle" options as well as scheduled backups. Very easy to leave running and forget about until disaster strikes and you can recover your docs. You can also throttle between certain hours - useful if you ISP has off peak times.
Other services are also available:http://www.xdrive.com/
Xdrive gives you 5MB of free online storage.http://www.idrive.com/
Idrive gives you 2GB for free.http://www.drivehq.com/secure/Signup.aspx
Drive Headquarters gives you 1GB free.
Not sure what effect having all these running scheduled jobs to back up different file sets would have but there is potentially 10GB of free secure online storage there - enough for most photo and MP3 collections.