This is a list of all the newspaper-specific databases we subscribe to at Mac. Hover over the "i" on each to see what coverage they offer. Also note that many of the primary source databases in the column to the right also contain newspapers and other periodicals.
Wikipedia has a list of newspapers that are available online, sorted by country. Keep in mind that this list could be out of date and/or incomplete.
Hint: When searching the library catalog, try adding one of the following words to unearth primary sources: