Here are sources of datasets on a wide variety of subjects.
ARDA: Association of Religion Data Archives - data and GIS maps of religious denominations in the U.S. and worldwide
(U.S.) BLS - Bureau of Labor Statistics
GESIS - European and international data
Google Public Data - visualize data analysis.
NHIS - National Health Interview Survey
Pew Research Center - access to data sets available with free registration.
SAMHSA: Substance Abuse and Mental Health Services Administration Data
UNC Dataverse / Odum Institute Data Archive - open repository of social science data sets, including state-level polling data