"Open-access (OA) literature is digital, online, free of charge, and free of most copyright and licensing restrictions."
Peter Suber, "Open Access Overview" http://legacy.earlham.edu/~peters/fos/overview.htm
Browse open-access (OA) literature at Rhode Island College in DigitalCommons@RIC
There is no evidence that it has or will, although it may become more difficult for publishers to sell journals to libraries at extremely inflated prices. Still worried? read: "The Death of Scholarly Journals?" by Stuart Schreiber on his blog The Occasional Pamphlet on Scholarly Communication.
In 2002, the U.K. Research Council created a new organiation, SHERPA "Securing a Hybrid Environment for Research Preservation and Access." Among other projects, SHERPA began to record journal publisher policies. They created a searchable database of publisher's policies regarding the self-archiving of journal articles on the web and in Open Access repositories. The collection of “Rights MEtadata for Open archiving” became known as RoMEO.
Because the major research publishers are international and many European universities went Open Access nearly ten years ago, most publishers have already gone green or at least blue in order to keep authors.
Use the Sherpa/RoMEO site to find a summary of permissions that are normally given as part of each publisher's copyright transfer agreement. Search by Publisher or Journal title. Or, Ask a Librarian to advise you.
Suber, Peter Open Access: Six Myths to Put to Rest The Guardian (October 21, 2013)
Howard, Jennifer Open Access Gains Major Support in U. of California's Systemwide Move Chronicle of Higher Education (August 2, 2013 )
Mechanic, Michael Open-Access Champion Michael Eisen "Sets Free" NASA's Paywalled Mars Rover Research Mother Jones (Sept 30, 2013)
Vaughn, John (2013) "The future of scholarly communication: US efforts to bring warring factions to common purpose in support of scholarship" Information Services and Use. 33(1) 27-36