Just like the movies did not kill the novel industry, the TV did not kill the movies, the radio did not kill the record industry, photography did not kill painting etc I think that all that exists is going to survive albeit in a redesigned or resized form.
Just like radio is still a very present part of our lives, even if it certainly doesn't have the importance it had in the 1930s, so I think newspapers and magazines will survive, adapting to their niche, some of them betting on content quality, some other on printing quality (you cannot beat a well printed photography magazine with an e-book) some other on specialist nature of content.

Newspapers of the past were a very inefficient way to distribute information. You pay the entire newspaper, but it is a well-known fact that many people only bought them for the classifieds, or the sport, or the weather, or the gossip page etc. Newspapers would sell because they gave a different product to different audiences. They would throw in the crosswords, the comics or the horoscope because anything can help selling.

Here in Italy most newspapers, even the most serious ones (imagine the horoscope in the Financial Times or the Wall Street Journal), had the horoscope because it was obvious that if you had no horoscope you would loose clients because some wives would insist with their husbands (in any social class) that they buy a newspaper with the horoscope.

Internet gave people a cheap and practical way to know about cinemas, weather, local sport events, local news, horoscope, classifieds and all those "ancillary" information that were actually a big part in the sales of the newspapers. That said, I don't think printed matter will ever disappear. Not even books albeit menaced by e-books.