The whole "Oooh! Libraries are OBSOLETE, the world is DIGITAL now!" thing bugs me for four reasons.
(1) You know a lot of people actually like books that you can hold in your hand, right? And that there exist large numbers of books that ONLY exist in that format and haven't been digitized yet?
(2) Libraries have often been the centers of digitization efforts. Yes, you can find ancient papyri online. This is largely because of efforts like the one at the papyrology department at the University of Michigan library. The same is true of a bunch of other things.
(3) A lot of people have a library involved in their digital explorations, whether using machinery and connections AT the library because all they have is a phone, say, and perhaps a heavily metered connection, to access subscription only databases and archives, and to get help with research.
(4) They provide nuclei for community interaction, often around topics that improve people's relationship with knowledge.