That's why backing up your data is vitally important and while I'm mainly going to describe my photography back-up processes, it's equally important to back-up your personal files and folders as well. This is purely my advice, and it's what works for me, so hopefully it will help shed some light on what can be a confusing subject.
After shooting a load of images the first thing to spring to mind is to download the files onto my laptop. But, before I even do that I plug in my flash drive as that's going to be my first stage in the back-up process. Personally I use Adobe Lightroom to import my photos from the memory card and it has a great little option on the Import screen called "Back-Up to" which allows the files to be copied to another location, in this case my Flash Drive, as they are imported onto my hard disk. If you're not using Lightroom then it's simply a case of copying the content of the memory card straight to the flash drive with drag and drop.
After importing, all my images are now in an appropriately named folder within "My Pictures", similarly stored on the flash drive and still on the camera's memory card. Now I burn these originals to a DVD, again stored in a suitably named folder. So why do I bother with the flash drive stage if I'm going to burn them to DVD anyway? Well, every now and again I pop a blank DVD in the drive and it's a dud and won't work. I'm more often than not doing this in a hotel room somewhere and don't carry lot's of blanks around with me so it just means I have a separate, albeit temporary, backup should there be problems with a DVD.
So I now have my files on DVD, which is now my primary back-up, and also on the flash drive. I'll leave them on the camera's memory card until I use the camera again at which point I'll format it for a clean start. I'll then do my post processing work within Lightroom at the end of which I'm ready to move the files onto an external hard drive. I move them off my laptop's hard drive to keep as much space free as possible and therefore maintain performance. By doing this within Lightroom, it will still keep track of the images by associating them with being on the external hard drive. Finally I plug the external hard drive into my desktop computer at home and copy the images into a similarly structured folder on it's hard drive.
At the very least I always have copies of my images on an external hard drive, a separate computer's hard drive and on DVD. I know some people would argue this isn't enough and indeed I know of people who keep another external hard drive at a friend's house just in case their's burns down! But this works for me for now, though I might just invest in another external drive at some point, just in case!
The key thing in all this is to have your files saved to different external locations such as DVD, External Hard Drive, Flash Drive, separate computer etc. Having everything on only one computer, as thousands of people do, is just too risky. If that machine is damaged, stolen, or fails, it's a nice feeling to know you can get all your stuff back again. How you exactly do that is another story!!