Researchers in the United States are spoiled with access to newspaper “mega sites” like Newspapers.com, GenealogyBank, and News Archive. They’re not free, but they do have a broad geographical reach. They do not hold all available newspapers, but they represent at least some newspapers from every U.S. state and sometimes other countries. A one-year subscription is reasonably priced. This concept does not exist in Germany.
Some German subscription newspaper sites do exist, but differ in scope to American mega sites. Historische-Zeitungen-Bestellen [Historical Newspaper Ordering] is an example of a German website that allows you to find and purchase one issue of a newspaper for €39.95. This is intended to be used as a gift for a birthday or other special occasion. This is not economical for the average genealogist researching multiple family members. Recently, a new subscription website became available, Archiv der Westfälischen Nachrichten [Archive of Westphalia News]. It contains newspapers from that region from 1946 to the current time. If you research in the North Rhine-Westphalia area, you might want to check that out.
The good news is there are historical German newspapers that are digitized and online. Many of them are free. Some are searchable and others are only browseable. Ernie Thode published a book about these newspapers in 2014, Historic German Newspapers Online. His book identifies over two thousand newspapers that may be accessed via the internet. They all are written in German, though many were published outside Germany, including the United States.
For listings of online newspaper archives related to German or German language newspapers, see this Wikipedia article: https://en.wikipedia.org/wiki/Wikipedia:List_of_online_newspaper_archives#Germany
Many of the above resources link to collections also identified in Thode’s book. If you need newspapers pertaining to your area of research, consider state libraries and archives of the region. Every modern German state has at least one archive. Use the German Archive Portal to easily find them.
Many German universities have digitized newspapers. Universities with collections include the University of Bremen, University of Düsseldorf, University of Göttingen, and University of Münich, to name only a few.
The Allgemeine Auswanderungs-Zeitung was published in Rudolstadt, Germany. The Technical University of Jena houses digitized issues spanning 1846–1859 on their website. The January 1849 issue showed summary lists of ships that left Bremen bound for North America in 1848. Earlier research informed me that Joseph Steinkamp, my great grandfather, and his one chest sailed from Bremen, arriving in New Orleans on 12 November 1848. Thanks to the newspaper summary, I know the ship left Bremen 20 September and Joseph was at sea fifty-three days with 180 other passengers. This example shows how newspapers may not name your ancestor, though they can detail events that directly impacted them.
While German newspapers require a bit more research to find, they hold valuable information. Explore the newspapers that are available for your research areas. You never know what goodies you might find. I hope you find this helpful (and inspiring).
 “Übersicht,” Allgemeine Auswanderungs-Zeitung (Rudolstadt, Germany), January 1849, no. 6; digital image, Technical University of Jena (Thuringia) (http://rzblx1.uni-regensburg.de/ezeit/detail.phtml : accessed 6 January 2017).
 Manifest, Bark Post, 10 November 1848, line 102, Joseph Steinkamp; digital images, Passenger Lists of Vessels Arriving at New Orleans, Louisiana 1820-1902 (http://www.ancestry.com : accessed 20 May 2004).