We advise that you copy your image files on multiple storage devices such as DVDs, external hard-disks, and flash-drives (USB sticks). Keeping your images on a single device is extremely risky, as both DVDs and hard-disks fail very often, and USB sticks can be lost. The average lifespan of DVDs and hard-disks is between 5-10 years. With regards to external hard-disk drives, we advise using external drives with dedicated power cord (also called non-portable external hard-disks, or AC-powered), as they tend to be more reliable than the portable ones that do not have an AC plug.
You may also consider an online backup solution such as dropbox, or box.net (both of which offer a free account) or crashplan, which offers a yearly subscription package for unlimited storage. If you plan to backup the images online, please make certain the service you are uploading to does not process the images in any manner that reduces their file-size or strips out ICC data, as this will alter the colours and quality of the photos. (As an example, at the time of writing this, Google drive strips out ICC-data, and as a result changes the images’ colours).
You might also be interested in this post on our blog discussing prints as the ideal archiving method: http://sweetmamaphoto.com/why-it-is-important-to-print/