Once when I was a teenager, I had a friend whose father was a pressman for the newspaper. We went downtown one day to visit his father at the newspaper. I remember going into the huge press room where the noise was so loud that you could not hear when shouting. I think that the newspaper press was one of the largest, noisiest, and most complicated machines I had seen up to that time in my life. I always remember the old movies and TV shows, when something was happening, they would always show the presses running and a copy of the newspaper, showing the headlines would come spinning out until it showed on the screen, to emphasize the importance of the event. Presses still run and they are still loud, but the only spinning newspapers I have seen lately are in old movies.
Phoenix used to have two daily newspapers, the Arizona Republic, and the Phoenix Gazette. Now there is hardly one. If you want to get some idea of the impact of the digital age on print newspapers, look at the Wikipedia article, List of defunct newspapers of the United States and the website, Newspaper Death Watch. The only newspaper I see now is a free advertising paper thrown on my driveway three or four times a week.
Realizing that print newspapers are disappearing rapidly, a partnership between the Library of Congress and the National Endowment for the Humanities created the National Digital Newspaper Program. The U.S. Federal Government is not alone in its interest in preserving its newspaper heritage, individual states have similar projects and many other countries of the world have adopted aggressive programs to digitize existing newspaper collections. In addition, there are significantly large private commercial collection efforts. There is a list of national projects online at Wikipedia.
In my experience, genealogists tend to think of newspapers in a very limited way, mainly as a place to look for obituaries. Very few researchers have made extensive use of the newspapers' content in their research. But the newspapers' content stretches way beyond obituaries. Newspapers were the daily diary of the world. Especially in small towns, newspapers were the Facebook of their day and told the story of the families living in the circulation area. Today, most who see some of the old newspapers for the first time, are amazed at the rich detail in their pages.
Some public libraries, many historical societies and some museums have collections of old newspapers moldering away in basements and storage areas undigitized. It is still too early to tell if the digitization efforts will stem the loss of these valuable records. It is a fact of life that newspaper were printed on cheap, high acid content paper and if left unconserved, the papers will disintegrate over time.
The first go-to place for newspapers in the United States, is the Library of Congress. The Chronicling America, National Newspaper Project, has millions of pages of completely indexed newspapers online as well as a Directory of all the papers published in America from 1690 to the present. In every country where there is a similar project you can find collections of newspapers. For example, the National Library of Australia (NLA) provides free searchable online access to digitized copies of out-of-copyright Australian newspapers (1802–1982). The NLA list of available titles includes more than 50 capital city and rural newspapers. There are many, many more examples.
In the U.S. there are also online, usually commercial subscription services such as MyHeritage.com's WorldVitalRecords, Newsbank.com (GenealogyBank.com) and many others.
Hopefully, when the presses stop rolling for the last time, we will still have our legacy of newspapers to research.