The Inter-University Consortium for Political & Social Research (ICPSR) is a membership-based organization, with hundreds of member colleges and universities around the world. The consortium supplies data files for use with statistical software, such as SAS, SPSS, and Stata.
The ICPSR data holdings contain some 6,000 studies and 450,000 files that cover a wide range of social science areas such as: population, social & political attitudes, crime, social & political behavior, substance abuse, and more.
You will need basic statistical skills for using online analysis tools and more advanced skills for running your own analysis.
NOTE: You will need to set up a profile with ICPSR in order to gain full access to the datasets. You will need to be on University of Dayton IP (on campus, generally) to create the initial profile; afterwards, you can sign in from any access point.