General Social Survey (GSS)
The GSS measures public opinion in the United States on a wide variety of topics of interest to social scientists. The survey, which began in the early 1970's, provides a biennial perspective on American attitudes toward government, life, race, religion, and other social issues. The link here is to the GSS homepage within the National Opinion Research Center. Sites where researchers can extract and download specific variables of interest are listed here. The SDA Archive at Berkeley also holds GSS data from 1972 to 2016 in an interface that allows for basic on-line data analysis and the creation of subsets of GSS data. GSS data are also available via the Roper Center.
National Archive of Data on Arts & Culture (NADAC)
The ICPSR's National Archiv of Data on Arts & Culture contains many datasets pertaining to topics such as participation in the arts (e.g. attending exhibits or concerts), "cultural policy" (e.g. support for public funding of the arts), the vitality of the arts in local areas, and media coverage of the arts and culture. Much of the contents of this archive formerly resided at the Cultural Policy and the Arts National Data Archive (CPANDA).
Pew Research Center for the People & the Press
The Pew Research Center for the People and the Press is a major center for the study of public opinion and regularly conducts polls about various social and political topics and contemporary issues. They make many of their studies available for download here. Many of the more recent datafiles are in SPSS format. Users are required to register before downloading a dataset, but registration is free. Users should also check out the resources available via the Pew Research Center homepage for other collections of public opinion data, such as Hispanic Trends, the Global Attitudes Project, and Religion and Public Life.
Roper Center for Public Opinion Research
The Roper Center is one of the country's premier centers for polling data, with holdings dating back to 1935. While the bulk of the Center's data are for national polls, it also includes many state-level polls as well and collects data from a wide and eclectic range of organizations. The iPOLL interface may be of particular use because it allows users to search through surveys at the question level. Roper also has a large compilation of Presidential approval ratings. The Roper Center is also available via Databases at Emory.