JSTOR (short for Journal Storage) is an online system for archiving academic journals. The non-profit organization provides its member institutions full-text searches of digitized back issues of several hundred well-known journals. The latest issue of a journal available in JSTOR is usually 3 - 5 years behind the current date.
NB: JSTOR supports full text keyword searching only. So your search results are only as good as your search terms.
In January 2012 JSTOR announced "Register and Read," a beta experiment. It will give at no charge limited access to all the articles in 70 journals that account for 18% of user demand. Registered guests will be able to read (but not download) three articles every two weeks.