The Center for Research Libraries in Chicago has an extensive collection of German newspapers in microfilm. To find them, search CRL's catalog for "newspapers" and then under the tab for newspapers, search by the title of the newspaper. To get access to the microfilms, order them through the Library's Interlibrary Loan and Document Delivery.
(2015) Newspapers in German Language – Progress in Digitisation and Accessibility. Paper presented at: IFLA WLIC 2015 - Cape Town, South Africa in Session 80 - News Media. In: IFLA WLIC 2015 - Cape Town, South Africa http://library.ifla.org/1265/
The UIUC Library has a very extensive collection of newspapers, both current and retrospective, in a variety of formats, including hard copy, microfilm, and digital reproductions. Not all of them are included in the online catalog. Many newspapers can be found through the Library Gateway.
Some newspapers that are not found in the online catalog may be included in the Library's separate online database of newspapers. This database is searchable by place of publication and by keywords from the title. For German studies, try indicating a particular German-speaking country, or simply search for all German language newspapers.
A further resource for finding German newspapers is the Center for Research Libraries. Their collections are particularly strong in German-American newspapers (Historical newspapers published in the United States in German language). You can search for these publications in the CRL catalog.
Titles from Germany, Austria, and other German-speaking countries are represented below.
Bayerische Zeitungen (1848-1850) - newspapers are organized by region (Altbayern, Schwaben, Franken)
Digitale historische Tageszeitungen (GenWiki) - a major genealogy wiki provides links to various digitized newspapers. The listing is organized by region.
Das digitale Zeitungsarchiv der Landesbibliothek Dr. Friedrich Teßmann - digitized newspapers from the Alpine region. Several titles are from the south Tyrol region (newspapers in German and in Italian)
Friedrich-Ebert-Stiftung - retroactively digitized papers from the 19th and 20th centuries.
Heidelberger Zeitung - 19th and 20th century coverage of newspapers from Heidelberg.
Internetarchiv jüdischer Kulturbund (1806 - 1938) - covers over 100 Jewish periodicals in German. A highly recommended resource!
Liechtensteinische Landesbibliothek - full-text searching of various 19th and 20th century newspapers from Liechtenstein.
Pressemappe 20. Jahrhundert (1900–1945) - review dates and actual titles on this one.
Provinzialbibliothek Amberg: Digitale Sammlung - includes the Amberger Zeitung as well as other fascinating materials.
Staatsbibliothek zu Berlin - list of digitized newspapers, various 19th and 20th century titles. Left navigation bar includes a special section for daily newspapers from the GDR.