Dryad 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. Data are searchable by placename, subject, journal, institution, as well as keyword.
Figshare is an online, cloud-based, multi-disciplinary repository. Featured categories of research include: agricultural, veterinary and food sciences; biological sciences; biomedical and clinical sciences; built environment and design; chemical sciences; commerce, management, tourism and services; creative arts and writing; earth sciences; economics; education; engineering; environmental sciences; health sciences; history, heritage and archaeology; human society; indigenous studies; information and computing science; language, communication and culture; law and legal studies; mathematical sciences; philosophy and religious studies; physical sciences; and psychology.
FiveThirtyEight has shared the data and code behind some of their articles and graphics.
Harvard Dataverse is a free data repository open to all researchers from any discipline, both inside and outside of Harvard University, where you can share, archive, cite, access, and explore research data.
OAD (Open Access Directory) Data Repositories lists open data repositories for: archaeology, astronomy, biology, chemistry, computer science, energy, engineering, environmental sciences, geology, geosciences and geospatial data, linguistics, marine sciences, medicine, multidisciplinary repositories, physics, and the social sciences.
Open Domain-Specific Data Sharing Repositories lists National Institutes of Health-supported domain-specific data repositories that make data accessible for reuse and are open for both submitting and accessing data. Submission to the various repositories are typically limited to data of a certain type or related to a certain discipline. A few data repositories on the list:
Re3data.org is a global registry of research data repositories that covers research data depositories from different academic disciplines. It includes repositories that enable permanent storage of and access to datasets to researchers, funding bodies, publishers, and scholarly institutions.
ResearchDataGov is a "web portal for discovering and requesting access to restricted microdata from federal statistical agencies."