You may have heard of LexisNexis, the giant full-text, searchable database of newspapers, magazines, legal documents,and other printed material It’s used extensively by journalists, law students (and lawyers), as well as a variety of student researchers.
Lexis.com is geared primarily to law, while Nexis.com covers the non-legal branches. While no website offers full-text archive searching for free (outside of those with access to a college or University that has subscribed to the service), there are ways to get much of the information for free.
Current Newspapers: http://www.abyznewslinks.com/ ABYZ News Links provides a listing of thousands of newspapers, along with their location and their URL.
Newspaper archives (free/pay-per-view) http://news.google.com/archivesearch Google News will allow you to search for news articles in both free and pay-per-view sources. While the amount of free articles returned is debatable, it will allow you to identify a newspaper and article time/date for use with another system.
Magazine articles: http://books.google.com/books?id=tuMDAAAAMBAJ Google Books provides several archives of magazines online. The included link is to Popular Mechanics. A listing of several of them can be found at Wikipedia here.
Legal decisions: US Supreme Court, a variety of other US Courts. Supreme Court of Canada decisions. A variety of other Canadian courts.
While no resource quite matches LexisNexis’ convenience and breadth, I hope these websites will allow you to learn a little less expensively.