Public Libraries continue a noble purpose: to provide community access to resources that would otherwise be unavailable.
Often this boils down to money-- most individuals can't afford vast libraries of diverse materials on their own, so they pool their money (in the form of taxes) and share what they buy (in the form of public libraries).
Unless the capitalistic nature of our society is radically altered it is unlikely that new and desirable resources will ever become freely available to everyone. So, regardless of the formats the resources take, the need for public libraries (in one form or another) will continue.
And, as always, public libraries will collect what their constituents want and develop the most effective means to deliver the goods.
Digital formats are part of the evolution of information-sharing, not really a revolution (granted, the evolution has speeded up considerably since the heyday of the papyrus scroll). So I'm not worried-- libraries and librarians aren't facing extinction but will continue to evolve as well. The more information that is available, the more people need teams of information professionals to help them find what they seek.
We (JPL) have embraced digital formats and work to expand our digital collections. The Internet provides the ideal avenue for digital delivery, and we try to take full advantage of it, including granting free access to non-residents via free eCards. Only ...
Our immediate problem is marketing-- we have all these really great databases and online services available, and are providing more and more downloadable materials. But sooo many people remain unaware of them, even those who routinely use the Internet for virtually everything (pun intended).
Another thing-- why don't we (JPL) have scanners so we can e-mail copies from print items rather than faxing them? (E-mail is one of the most universally accepted delivery methods, is one of the greatest advantages the Internet offers, and is way more reliable than using outdated fax machines--not taking advantage of the available technology just doesn't make sense.)