A month or two ago I added a DNS-321 network storage device. I moved all of our photos, documents, music, etc onto this device. Since this box has twin mirrored drives, there is some protection from physical drive failure. However, it doesn't have "previous versions" (which you'd have on a drive on your windows machine), plus if there is a fire, flood, theft etc I'd still lose my data. So, the final component is to add an off-site backup.
The most convenient and fail-safe method seems to be an online backup service. At work we use mozy.com, but mozy seems to be focused on business backup. One of my co-workers uses idrive, and had good things to say. So, today I signed up and started the backup process.
Essentially, for the initial backup it takes a long, long time to copy all of your data onto their secure servers. Once the initial backup is complete, each night it looks for new or changed files and only uploads the new files. Easy and relatively cheap, $4.95 per month for 150 Gb of storage.