Repositories are online resources that allow researchers to place their data in a secure location in order to enhance sharing and to meet mandates of granting agencies. These are also resources for locating data sets. Many repositories are discipline-specific, though some generalist repositories are also available. The University of Michigan Library provides Deep Blue Data, a data repository for U-M affiliated researchers of all disciplines.
Sometimes data generated for one purpose can be used again with new questions and new investigations. One must consider methodological differences, ethical concerns, and potential copyright issues when re-using data. Often if you want to re-purpose data, you will need to develop a Data Use Agreement. The UofM Office of Research and Sponsored Projects offers some basic guidance in this endeavor. The Stanford University Privacy Office provides a useful explanation of Data Use Agreements. In some cases, you may create a 'limited data set" from the original data by stripping out certain data elements, perhaps due to privacy concerns or other sensitive content.