Here is a site with links to digital online newspapers from around the world, many of which are free http://icon.crl.edu/digitization.htm . The pay sites are clearly marked with a dollar symbol in a circle.
I have used Colorado Historical Newspapers & Utah Digital Newspapers for a few years and found some real gems. One hint is 1st search by name & time period, but if that doesn’t work I have had good luck is searching by date only. Say you have death date, search in that paper just after the event then look in the next 3 papers. Smaller papers will have sections for local news for different towns & if it is a real small paper death & marriage will be front page news.