The following are databases of data centers and subject-based data repositories.
NIH Data Sharing Repositories
The National Library of Medicine has produced a table of NIH-supported data repositories.These repositories do accept data from non-NIH research. There are 45 repositories listed.
re3data.org The Registry of Research Data Repositories was released in December 2012. The registry is a result of a partnership among the Berlin School of Library and Information Science, GFZ German Research Centre for Geosciences and the KIT Library of Karlsruhe Institute of Technology. The initiative is being funded by the German Research Foundation DFG.
FAIR stands for Findable, Accessible, Interoperable and Reusable. These are principles being promoted in order to develop standards ensuring that datasets resulting from government funded research are available. For additional information see FORCE11 and an article in Nature, The FAIR Guiding Principles for scientific data management and stewardship. This FAIRsharing resource provides access to databases and in addition indicating the standards and policies used to develop the databases/repositories.
Open Access Directory The Open Access Directory of Data Repositories is being maintained by Simmons College.
In addition both Nature and PLOS have lists of recommended repositories.