Full disclosure: this is an assigned topic. I'm in a master's program to get a degree in library science -- there really is more to it than just alphabetizing books -- and one of my assignments is to create a blog and post an entry with my thoughts on how e-readers will affect libraries. I was already half way there because I just happened to have created this blog about a month ago, and it was so kind of my professor to gift wrap the topic for me because being assigned doesn't mean it's boring. And so, on to libraries and e-readers.
Libraries are always expanding and chronically short on space for their collections. Take the public library I used growing up, for example. It had started in an old, pioneer era building that had been added on to and haphazardly modernized over the last fifty or so years. It was stuffed to the gills with towering, nearly full bookshelves, and there were hardly any reading areas and no room for expansion. When the city finally built a new, larger library, the thing that struck me most was all the empty shelf space. Having been filled to capacity for years, the librarians made sure that they had plenty of room for the collection to grow when they moved to the new space, and a huge portion of the available shelves sat empty, patiently waiting future need. This is the cycle you see in any type of library, and it is a cycle that e-readers have the potential to completely change or even do away with. Obviously, electronic media don't need vast amounts of shelf space (for example the automated retrieval barns found in many academic libraries) and this could open up huge opportunities for libraries that have always been constrained by the physical space available to store their collections.
On the other hand, e-readers and electronic sources of information have the potential to completely bypass the library on the book/information's path from source to consumer. If a person can purchase and download any book instantly from an online source, why would the library need to be in the picture at all? The opportunity I see for libraries is that they can become the the source to which the consumer goes to download that e-book. Just like with paper copies of the books, people will want to borrow, not permanently buy, many of the books they read, and that is where your friendly public library will step in. By providing access to huge electronic collections, they can reinstate themselves in the information loop. I know there are problems with the current method of delivery for e-books. The licensing of the materials and the ways that they can be used by libraries are limited, but progress is being made in making it easier for libraries to purchase multiple licenses and share the media with multiple patrons, and once that is all ironed out, huge possibilities open up.
And, as a final note, one definite plus about e-books rather than paper ones is that you can be sure another person hasn't read it in the bathroom. It's a silly thing I know, but one that might add to a lot of people's peace of mind when patronizing the public library.