You should take an active role in managing your own copyright.
While you are not required to register your copyright, there are some benefits to registration. Registration creates an official record, helping others identify the copyright holder and helping in any legal dispute.
When you publish, you are not required to assign all your rights to your publisher. Consider how you may want to use your work in the future, or how you may want to make it available to others. You can "unbundle" the rights included under copyright, assigning some to your publisher and retaining others. SPARC, the Scholarly Publishing and Academic Resources Coalition, advocates for author rights and provides an author addendum modifying copyright agreements with publishers.
Using a Creative Commons License grants permission to others to use your work in specific ways. Several levels of license are available.
To make your work most accessible to others, consider Open Access publishing.
Note that many government agencies require that the results of research they have funded be made publicly available.
See the White House directive on public access to the results of research and information on the Fair Access to Science and Technology Research Act (FASTR).
University of Missouri policy on patent & copyright law deals with issues of whether the student, instructor, researcher or University hold the copyright for work done at the University.