Historical Newspapers from the Library of Congress
The Library of Congress and the National Endowment for the Humanities have a joint venture that may be of interest to researchers and history enthusiasts. Chronicling America provides information on newspapers published since 1690 from across the U.S.
Use the Newspaper Directory to locate titles by location, date, or even ethnic or labor group focus. Once you've found one or more newspapers of interest, the site can help connect you with libraries in your area that own them. A search for Minnesota newspapers yielded some 3,000 title entries (though some entries were duplicates).
The site also includes digitized images of a set of newspapers, including the St. Paul Daily Globe from the late 1800s. Search for these on the Search Newspapers page.
This topic begs mention of several other resources. WorldCat, for instance, can help you locate and request newspapers via interlibrary loan. WorldCat is one of the ELM databases. Another excellent source is Minnesota Reflections. This site from the MN Digital Library provides online access to historical primary source materials including plat maps, diaries, letters, and photos.