I will miss the serendipitous discovery of information gained by casually browsing a newspaper. Kind of like reading a social news site. I rarely pick up a paper to read a particular article; I read for the sake of reading.
However, I disagree with the underlying assumption: newspapers are not going to go away completely. Instead, the industry will become strongly segmented into hyperlocal and national divisions.
Hyperlocal papers (the myriad 20k-circ dailies and weeklies) are doing great right now, primarily because they provide coverage of news and events that isn't available anywhere else.
A handful of national papers will survive, too, in order to satisfy those who still enjoy getting national news from dead trees (a segment that, while shrinking, is unlikely to completely disappear). My money is on The Wall Street Journal, USA Today, and perhaps The New York Times weathering the storm.
Mid-level papers, on the other hand, are doomed. They are the "mushy middle," satisfying nobody's needs well.
I used to work at a newspaper, and I feel sentimental about them, but emotion does not change business reality.