Some publications offer free, fully searchable archives. Some charge a fee for stories that are more than a few weeks old, and others don't maintain an archive at all.
Google now offers Google Book Search where you can search for and download out-of-copyright books. From Shakespeare's Hamlet to Jane Austen's Pride and Prejudice, download favorite classics in PDF form and read at your leisure.
For current news on dozens of subjects from thousands of sources, go to HeadlineSpot. The site lets you navigate the news by media type, subject and region. You can also use keywords to search the news on HeadlineSpot, or use a number of news search engines. HeadlineSpot also provides a list of searchable newspaper archives providing links to twenty U.S. newspapers' article archives.
If you're looking for articles from a particular publication, visit a magazine, newspaper or journal index to see what that publication offers from its site.
For articles in general, try Britannica.com. The information supersite will simultaneously search for select full-text articles, Web sites and encyclopedia entries that match your keyword.
Still empty-handed? See if your public library offers access to full-text databases or consider a free trial of Electric Library, which offers the full text of many magazines and newspapers online.