Originally every author owns their own work, but authors are often asked give away those rights through an "author agreement" during the publication process. Your choice to relinquish rights to a publisher has implications for who can read your work, whether you may use it in future work, or even share it in class or on the web.
An "author agreement" is often available on the publisher's web site or the web site for the journal. These documents include information on whether authors retain the right to re-use the work or post it on their own web site. Authors who wish to retain more rights than the publisher's author agreement allows often consider the use of an addendum. See the SPARC addendum section.