Carolina Population Center (CPC)
https://www.cpc.unc.edu/
UNC-Chapel Hill's Carolina Population Center hosts multiple research projects related to the themes of demographics, population health, and reproductive health, in both the United States and elsewhere. See https://www.cpc.unc.edu/research-themes/projects/ for a full list of the CPC's projects. Public-use data from CPC projects are available via the Center's Dataverse, and you can also request access to restricted versions of data from CPC projects. The Center also provides a compilation of publications from its research and multiple tools for the collection and analysis of survey data.
Harvard Dataverse Network (DVN)
https://dataverse.harvard.edu/
Harvard's Dataverse Network is an eclectic collection of datasets and data collections, ranging from replication datasets from articles to institutional data collections. Many development NGO's and research organizations use Dataverse, including the Jameel Poverty Action Lab, Population Services International, Innovations for Poverty Action, the International Food Policy Research Institute, the Population Council, and the Center for Global Development. Dataverse also hosts more esoteric, specialized data collections, such as this collection of data on financial inclusion and access in Kenya.
ICPSR (Inter-University Consortium for Political and Social Research)
https://www.icpsr.umich.edu/
The ICPSR is one of the largest collections of quantitative data in the world. The archives contents cover a very wide range of topics, with household surveys, health conditions and health care, and public opinion being particularly strong points in the collection. Emory's local ICPSR representatives are Ms. Jennifer Doty and Dr. Robert O'Reilly. The ICPSR is also available via Databases at Emory. Please see this notice and these instructions from the ICPSR on how to access the archive and its data when off-campus.
Office of Population Research (OPR)
https://opr.princeton.edu/
Princeton University's Office of Population Research is "a leading demographic research and training center. OPR has a distinguished history of contributions in formal demography and the study of fertility change. In recent years there has been increasing research activity in the areas of health and wellbeing, social demography, and migration and urbanization." See the OPR's data archive for access to data from projects such as the Highly Skilled and Educated Immigrants, the Latin American Migration Project, the Mexican Migration Project, and the New Immigrant Survey.
World Bank Data Catalog
http://data.worldbank.org/data-catalog
As part of its Open Data Initiative, the World Bank has opened up access to dozens of its data collections and compiled into a single data catalog. The holdings here range from larger databases covering multiple topics to more narrowly-focused collections associated with particular research projects. You can also search for World Bank data by country or by looking for specific indicators.