Yesterday was World Backup Day. People around the world decided to create this website to remind people how important backing up your data is. Most people don’t know that a HDD – or even SSD – can fail, and ignore the fact that their house or flat can simply burn down or be robbed.
What I use personally is a Raid-1 Synology DS207+ with nighly synchronization to store the data that is very important to me – pictures, music and documents. I also have a Synology DS411j which I plan to upgrade to a Raid-5 configuration with 4x 2 Tb HDDs.
And for the really important stuff I simply use a Dropbox account. Saving in the cloud is still the safest bet, although some people will have privacy concerns. So what I would recommend is renting a low-priced server in a data center and setup a rsync there.
Whatever the solution you choose, simply make sure that you do have a backup plan before you need it.