Elephind is a search engine that searches across many newspapers from four different countries. If it indexes papers of interest to you, it could be a quick solution.
Many newspapers are now offering direct searches of their archives and paid access to their digital backfiles Here are some examples:
Many states offer online access to newspapers to residents of that state. Connecticut's iCONN service, for example, provides residents access to digitized backfiles of the Hartford Courant from 1744 to 1922.
While there are millions of pages of digitized newspapers, millions more exist only in print or on microfilm. Where are the Newspapers? provides guidance on locating copies of papers in the Cornell University Library.