Database tour: some of the big full-text sources
Early English Books Online
eebo.chadwyck.com. Most print in English up to 1700.
Eighteenth-Century Collections Online
Early American Imprints (Evans)
infoweb.newsbank.com/?db=EVAN&s_start=evans. The British colonies and the U.S. up to 1800.
American Periodical Series
search.proquest.com/americanperiodicals. Good for the U.S. 19th century.
search.proquest.com/britishperiodicals. Excellent for the British 19th century.
ProQuest Historical Newspapers
More specialized possibilities
Some I have used recently for research or teaching: Modernist Journals Project (modjourn.org), Pulp Magazines Project (pulpmags.org), African Writers Series (collections.chadwyck.com/home/home_aws.jsp)…