Pew Research Center provides data-driven reports and non-partisan public polling for social issues in the United States and (to a more limited extent) internationally:
(click on the image to see the full example report)
In order to see the different categories and world regions Pew has produced reports on, choose "Research Topics" near the top of the screen:
(click on the image to expand)
Linked below are a list of websites where you can locate statistics on various topics.