I use mine for backups. I've been saved more than once through having complete hard drive backups going back a long way; a full backup every week of selected folders on my main drive going back about a year.
The specific times I've used it, the most recent dozen backups didn't have the file I needed, as it was a file I'd deleted accidentally and not noticed for a while, or a file that had been corrupted and the corrupted file was being backed up for some time before I noticed.
I could burn DVDs and store them somewhere, but being able to have an automated weekly backup with a long archive makes both the backup and restore processes so much easier.
I also use the drives to store most of my data CDs (audio CDs are, naturally, ripped already). I find it far easier to find a .iso CD image and mount it than hunt through stacks of physical CDs for the one I want. This also means I don't have to worry about scratched disks.
Finally, Kije mentions saving off web pages. I don't do that, but I do save off application installers and web comics that I find interesting, as archive.org doesn't always pick up data and images.