DVD's can degrade overtime, and an external hard drive can fail. To really keep them safe, you either need to use multiple backups on separate devices (which can all burn in a house fire anyways) or store them online.
Unfortunately, if you store them online, when you upload them to sites like photobucket, they "shrink" your original file size (do they still do this?). Then, there is only one way to get your full sized photo back, BUY THEM!
I use a site called Smugmug. It is a prescription site, so you pay an annual fee for it. There is no adds, no limits to what you upload, and you can get all your files back anytime you want. I have thousands upon thousands of pictures on my account all at full resolution, mostly taken with an 18mp Canon 60D DSLR, so not small files.
It works for me, most don't like paying the annual fee, but for me it's worth it. I feel my pictures are as safe as they can be on the website. We also store them on a back up hard drive as a "just in case".