Europeana is a search portal of digitized collections from European National Libraries. Europeana contains also digitized newspapers from many European countries.
Great Britain
British Library Newspapers, part I-V, v. 1600-1950.
Available at the Helsinki University Library.
Austria
ANNO - AustriaN Newspapers Online
France
Gallica is one of the major digital libraries available for free via the Internet. Gallica is maintaned by National Library of France. It provides access to any type of document: printed documents (books, press and magazines) in image and text mode, manuscripts, sound and iconographic documents, maps and plans.
Search interface is only in French.
Germany
Munich Digitization Center Digital Collections: Daily and Weekly Newspapers, Scholarly Journals A collection of 1,196,941 pages of newspapers and other journals from Germany. (January 2017)
Staatsbibliothek zu Berlin: A list of digitized newspapers. You can browse the list according to newsaper numbers, no full text search.
United States
Chronicling America - Search America's historic newspaper pages from 1789-1963 or use the U.S. Newspaper Directory to find information about American newspapers published between 1690-present. Chronicling America Includes full text search and is free to use.
Newspapers.com - Very large newspaper archive mainly from United States, available with subscription.
Early English Books Online (EEBO)
Early English Books Online (EEBO) contains digital facsimile page images of virtually every work printed in England, Ireland, Scotland, Wales and British North America and works in English printed elsewhere from 1473-1700 - from the first book printed in English by William Caxton, through the age of Spenser and Shakespeare and the tumult of the English Civil War.
Early English Books Online database is a combination of several digitized collections and contains both fictional and non-fictional literature as well as official documents of the time, pamflets, calendars etc.
Eighteenth Century Collection Online (ECCO)
ECCO contains literature, texts and documents printed in Great Britain between 1701 - 1800. This collection is based on the English Short Title Catalogue. Primarily in English - also includes other languages. Full-text searchable - every word on over 33 million pages.