Pew Research Center
The Pew Research Center is a nonpartisan "fact tank" that provides information on the issues, attitudes and trends shaping America and the world. It does not take positions on policy issues.  See "The Databank" menu or the "Projects of the Center" section to view statistics and download data.

Polling the Nations
A compilation of questions and responses from more than 12,000 national, state, local and special surveys, conducted by 700 polling organizations in the United States and 70 other countries from 1986 through the present. Each record in the database consists of one poll question and the participants answers. Only 4 simultaneous users can access Polling the Nations.

The Roper Center for Public Opinon Research maintains a vast archive of 18,000 public opinion datasets.  The majority of datasets pertain to the U.S. but data from over 50 nations is also represented.  RoperExpress allows you to download the data and documentation directly from the Roper site.  You must register and create an individual account in order to download.