When working with sensitive data and information, work with IRB and the research informationist to ensure data can be shared responsibly.
ScholarlyCommons is the University of Pennsylvania's open access institutional repository for gathering, indexing, storing, and making widely available the scholarly output of the Penn community. ScholarlyCommons accepts data as long as file sizes do not exceed 500 MB. Contact us if you are interested in sharing your data with ScholarlyCommons.
ICPSR, or the Inter-University Consortium for Political and Social Research, maintains a data archive of more than 500,000 files of research in the social sciences. It hosts 16 specialized collections of data in education, aging, criminal justice, substance abuse, terrorism, and other fields. Penn is a member of the consortium which means you can deposit your social science data in this repository. If you have sensitive data, this a great option for you as ICPSR has options for keeping sensitive data only available to researchers who are affiliated with member institutions.
The Dryad Digital Repository is a curated resource that makes research data discoverable, freely reusable, and citable. Dryad provides a general-purpose home for a wide diversity of data types for any discipline. Data in Dryad is free to use, but there is a fee for submitting datasets. Read more about fees here. Dryad is most commonly used for data associated with published articles but they will take datasets even if they aren't related to a journal article.
The Open Science Framework, or OSF, is a free, open platform to support your research and enable collaboration. OSF can serve as a repository as well as a collaboration space where files can be given restricted access. OSF is a good resources for keeping your different project files together as well as allow you to share your data publicly.
Zenodo is a general-purpose open-access repository developed under the European OpenAIRE program and operated by CERN. It allows researchers to deposit data sets, research software, reports, and any other research related digital artifacts.
FigShare is a repository where users can make all of their research outputs available in a citable, shareable and discoverable manner.
Harvard Dataverse is a free data repository open to all researchers from any discipline, both inside and outside of the Harvard community, where you can share, archive, cite, access, and explore research data.
There are many repositories where you could submit your data. One way to find an appropriate repository is to search the Registry of Research Data Repositories (Re3Data). This site is not very user friendly, so please ask us if you'd like someone to go through the list with you. You may also want to check out the Wellcome Trust's suggested data hosting sites. Keep in mind this UK-based guidance and not all of it may apply.
See also DataVerse's Comparative Review of Various Data Repositories