go out of business? no. I know book lovers, and I'm in high school.
So, there will still always be a demand for them by the people who prefer the feeling of a book in hand.
Also, as of now, there aren't many digital libraries (as far as I'm aware... actually, they probably just aren't so mainstream yet).
But I feel it will be a long time before the end of books. I just don't like reading from an electronic device for an elongated period of time.