Available through December 2020 (changed from 2019), Access World News Research Collection (from Newsbank) is a resource that includes a variety of news publications worldwide. These sources include major national and international newspapers, as well as local and regional titles, and newswires, blogs, web-only content, videos, journals, magazines, transcripts and more. Note: Access is provided through the Washington State Library and ends 12/02/2020
Geographic Search - use the Map Search (its slow)

Excellent source for state/regional/US newspapers (including the New York Times) as well as English-language foreign newspapers and foreign language newspapers. Not really browsable. Includes legal and business information as well.

A database of over 800 fulltext newspapers. To search a particular newspaper, click on the Publications link in the upper left screen.
Geographic Search: Select Geographic Terms under the "Select a Field" drop-down menu

Full text of 300+ U.S. and international news sources. Includes the Wall Street Journal (1984 - current) and the Boston Globe
Geographic Search: Select Advanced Search, then use the Location filter.

US and Canadian business trade journals, i.e. the Portland Daily Journal of Commerce.
Geographic Search: Select Geographic Terms under the "Select a Field" drop-down menu

An interdisciplinary, bilingual (English and Spanish) and comprehensive full text database of newspapers, magazines and journals from ethnic, minority and native presses. Articles date from 1960 to the present.

The Left Index is a complete guide to the diverse literature of the left, with an emphasis on political, economic, social and culturally engaged scholarship inside and outside academia. Coverage includes more than 247,500 citations and abstracts (with some full text) and spans from 1982 and earlier

Shut down at end of 2017, but content still available on the site.
"New America Media is the country's first and largest national collaboration and advocate of 3,000 ethnic news organizations. Over 57 million ethnic adults connect to each other, to home countries and to America through 3000+ ethnic media outlets, the fastest growing sector of American journalism."

More recent Seattle Times articles can be found online via the Seattle Times website OR on microfilm (1896 (some earlier) -current) at AN48 S4 D36x .
Current and previous month print issues are available in the Current Journal Room, Terrell Library.

NY Times content is available in Lexis Nexis Academic (see above) - its searchable, not very browsable. The Times is also available in the Newspaper Source Plus database from 1985-current (Click on "Publications" and search for New York Times, or limit your search query to the New York Times by using the drop-down menu in the Select A Field box and choosing Source). It is also available in the Historical New York Times from 1851 - 2012 (link above)
Also available in the Holland and Terrell Libraries Microfilm (AN33.N4 N49x )

(For older articles, be sure to change the "Return articles added to Google News between" date to something that works for your search, i.e. 1/1/1901.)
For a list of newspapers in Google News Archive (with links) look here.
For help, look here.

Listing by state of newspaper titles available digitally, link to source, fee/free info

Older issues (back to 1962) available in print at JK 1 .C15 (1st floor, Holland Library).
Weekly publication focusing on American politics, including extensive coverage of Congress, legislation, voting records, and more.

Older issues (back to 1969) available in print at JK 1 .N28 (1st floor Terrell Library).

Microfilm: 1958-2003 at call number AP2 .T37 (Holland Library 1st floor)
Print:

Microfilm: 1942, 1959-2003 available on microfilm at call number AP2 .N6772 (1st floor, Holland Library)
Print: 1933-2012; 3/2014-(current) at call number AP2 .N6772 (1st floor, Terrell Library).
Note: most recent issues are in Current Journals.

Note: Suspended print publication with v. 160, no. 27 (December 31, 2012) and resumed with v. 162, no. 10 (March 14, 2014). Vol. 161, no. 1 (Jan. 4, 2013)-v. 162, no. 10 (Mar. 14, 2014) were issued only online as: Newsweek global.

The Atlantic, the New Yorker, Vanity Fair, the Nation, Harpers, Scientific American, and more...