Plagiarism presents the same issues online as in the classroom. For MSU policies, visit http://www.msu.edu/unit/ombud/plagiarism.html
Make sure your syllabus specifies instructor expectations. Make sure students are aware of consequences for non-compliance.
MSU Example
Policy on Submitting Work from Other Classes as Your TC 841 Assignments
I expect the work you turn in for TC841 to be unique to this class unless you ask permission in advance to prepare the same assignment for more than one class. However, I encourage you to use TC841 to make progress on your thesis projects or to develop research plans for media production projects. So, don't turn in the same paper as you do for other classes without asking permission first, but do look for ways to make TC841 assignments useful and relevant.
This practice is not explicitly prohibited in the Academic Integrity Policy. If instructors find this unacceptable, they need to specify consequences in the syllabus.
Following are some commercial strategies for deterring plagiarism:
Turnitin and iThenticate offer a technological solution. They are being used by educators to combat plagiarism.
Go to plagiarism.org for a discussion about such technological tools and solutions.