Data publication will always involve granting some kind of rights of use to the data distributing agency because these agencies require non-exclusive rights in order to backup or distribute your data. However, transferring exclusive rights to third parties upon publication should be avoided. This is especially important if data are published as a supplement to journal publications, because publishers often demand exclusive rights for this publication mode.
Note that you waive all copyrights on your data by assigning CC0 licenses to it. You should bear this in mind as CC0 is the default license option of some repositories for research data (e.g. FigShare, Dryad or OpenICPSR).
- See the Creative Commons homepage for more information on their licenses.