ICPSR maintains a data archive of more than 500,000 files of research in the social sciences. Here you can find data on public opinions and attitudes on a variety of subjects from the presidency to the economy, and many more. Downloadable as SPSS, SAS, STATA, SDA, R.
Reported voting and registration, method of voting, and reasons for not voting, by various demographic and socioeconomic characteristics at national level for election years, 1964-present, from the Current Population Survey (CPS). Does not include partisanship or candidate choices.
National Voter Turnout data from 1828-2008. Available from the data archive of the American Presidency Project (americanpresidency.org); a collaboration between John T. Woolley and Gerhard Peters at the University of California, Santa Barbara.
Voter turnout data from primary and general elections 1980-2012 broken down by State. Data is collected by Dr. Michael McDonald, an Associate Professor at George Mason University and a non-resident Senior Fellow at Brookings Institution.