This might be more of a technical than philosophical discussion, on the surface; but ask 10 photographers about this, and I'm quite sure you'll get 10 different answers, ranging from 'why would I want to keep them?', to an underground vault in an undisclosed location. I'm probably somewhere in the middle, really - slightly on the side of the underground vault, if anything.
As a photographer, my images are important to me; not just when I take them, but for years afterwards, whether it seems that they have any future use or not. I can't count the number of times I've had a call, years after an image was taken, to see if I still have the file anywhere - often because one of the people in it has passed on, but mentioned that this was their favourite photo of themselves at some point.
Or, as has happened, when someone I photographed has won a major award - say, the Man Booker Prize - and suddenly, the world's media needs an image I took. And, of course, sometimes it's just a matter of wanting to find something for historical purposes: that time someone performed here before everyone knew who they were, and so on.
So, of course, I need to do my best for everyone I've photographed, so that I can help when moments like this come along. And the images not only have to be safe somewhere, I need to be able to find them as quickly as possible!
My strategy personally is not to use optical media like CDs and DVDs for my archives; for one thing, optical drives in computers are already disappearing, so the question has to be asked, how long will we even be able to read those discs?
I use the largest hard drives I can easily get my hands on, with the fastest available connection; and I never buy just one, always a second that can be stored off-site, and updated at least weekly. This solves a number of potential issues - RAID arrays or file servers, while useful in terms of redundancy, can still fail, be lost in a fire, or get stolen; and even if they can be repaired, within just a few years the parts become scarce, as happened to me a few years ago now when the motherboard of my computer caught fire one morning.
It took six weeks to find out that the parts needed to rebuild my built-in RAID array were unavailable; fortunately, I had done a complete backup only a day before it failed, so I barely missed a beat, but since then I've only used drives that I could replace easily, from a shop I can get to within an hour.
So I've got copies on hard drives in two locations locally; what about online, or in the cloud? I've used Photoshelter for over a decade, so the majority of my work is archived and searchable online already, and stored in two locations, on each coast of the US. (That said, I must confess that the majority of my own personal images aren't there yet, as I haven't needed to upload them for a client by a certain deadline. I must correct that!)
The big advantages to me about storing on readily-accessible hard drives are threefold: one, I can find anything I've ever done, pretty much immediately. All my images get metadata added to them as I import them, so they're searchable by some keywords, at very least by when & where they were taken. This search functionality is built in to Mac OS X, so it's not even always necessary to have specialist archiving & retrieval software any more - if your files are accessible to the system, they can be searched.
Two, if the drive starts to fail, I know right away and can replace it immediately. With optical storage like CDs and DVDs, there was no way of knowing when they started to 'go off', like bottles of old wine, because the temperature or humidity - or the pen used to write on them - were getting to them. At least with wine, you could look at the cork and see if it was starting to seep through, or see if the air level in the bottle had changed; with discs, unless you open each of them up on your laptop and check to see if the filesystem is intact, you'll never know.
And three, when the next storage technology comes along, transferring my many terabytes of data will be as fluid as possible. Instead of feeding endless discs into a drive and copying them onto some new kind of storage one by one, I'll drag one folder onto the next, leave it overnight, and be done by morning.
So, that's my personal strategy - immediate access, ease of verification, and fluidity of change. What about you: how are you preserving your archive?