We keep books because they are personal souvenirs of the past – physical reminders of the feelings we had while reading them.  The same goes for concert programs and tickets for sporting events, which many people keep.     As more of our life goes online, we risk losing such souvenirs.  Only the online record itself may provide a long-term reminder of something, or someone.
On the other hand, the web makes it vastly easier to bring to wide attention something or someone who should be remembered.  In the early days of photography, photographers recorded memorable events, such as weddings and Presidential inaugurations.  Susan Sontag noticed that something changed as photography ceased to be only done by professionals and became a democratic pastime: the relationship between events and photographs switched.  Now events were memorable (and remembered) precisely because they had been photographed.   The web is effecting the same reversal, I believe.
I can record a person of great influence on my life, who would otherwise be entirely forgotten to history, or people whom I never met, but whose words and actions have affected mine, for example, the activist-poets Vadim Delone, or Robert Southwell.  I can record people who think differently to the verbal paradigm which so dominates contemporary western culture – the  matherati, say, or musical thinkers.   I can even use the Web to find and trace the genealogy of some of my own musical thinking, say, and then record for posterity these cross-generational networks of connections.  Since so much of written history is by definition written by people au fait with language-based thought, it is particularly important that minority, non-language thinkers are not forgotten. (Many more people know, for instance, of the writers of Japanese haiku poetry in the Edo period than do of the ordinary people who solved temple geometry problems, the Sangaku.)
The souvenirs I mention above are mostly personal, perhaps of little interest to anyone else.  The same became true of photographs, early in their adoption.  The Web also lets us record for posterity events and people of much wider significance.   Perhaps the best recent example I know is Normblog’s admirable and riveting series of Holocaust stories, Figures from a Dark Time.  Apparently not everyone agrees that this series is worth doing.  Let me add my strong opinion that this recording is both necessary and important, and we should all be very grateful for Norm’s efforts.  After 9/11, the New York Times published short obituaries of every person killed in the attack.    Although it may be too late, we should be aiming for the same in remembering the Holocaust.