As the author of a work, you hold the copyright to that work, unless you transfer it to another entity. Most traditional journals require authors to transfer their copyright, by signing a copyright transfer agreement, to the publisher as a condition of publication. At this point, the author ceases to own copyright on the work that he or she created. This means that authors may surrender their rights to share their work openly on personal websites, etc. Recently, at least one publisher has exercised its rights to control access to the scholarship it published by sending take-down notices to the authors that created it.
Authors do have options available to them to ensure that they retain sufficient rights to make some version of their work openly available online.
Check SHERPA/RoMEO for a breakdown of most publication agreements (copyright transfer agreements) prior to submitting your work.
A publication agreemetn is negotiable! You can retain the right to make your work openly available through an institutional repository or personal website by attaching this addendum (PDF).
Most OA journals do not require you to transfer copyright to the publisher. Instead, they request a permission to publish your work and the rights reside with you.
The ARL Scholarly Communication Toolkit is a great place to start.
