Datawrapper Upload your data (as CSV) or copy/paste it into this free web application to make a quick chart that is publishable to the web.
Google Public Data Easily create line, bar, and bubble graphs from publicly available data sets and metrics.
Tableau Public Free downloadable software that works well with survey data, allowing you to filter data and recode variables, as well as create a variety of charts and graphs.
SDA (Survey Documentation Analysis) Developed at UC Berkeley, SDA is a web-based tool that is integrated into various collections of survey data, including the General Social Survey (GSS) and the American National Election Study (ANES), as well as microdata found in the Integrated Public User Microdata Series (IPUMS) which includes a more fine-grained version of Census data.
Gephi Open source platform for visualizing networks and complex systems, including dynamic and hierarchical graphs.
The following professional-grade software packages allow you to manipulate and visualize quantitative data in very complex ways:
How do I choose?
Choosing statistical software (online video, 36 minutes)
Choosing the correct statistical test in SAS, STATA, SPSS, and R Institute for Digital Education & Research, UCLA)
World Bank DataBank uses "bubble charts" to display social, economic, and health data from over 200 countries.
Gapminder is a tool for exploring and comparing global development indicators
Sunlight Foundation makes available a number of visualization tools related to politics and transparency, including "Lobbying Tracker" which tracks lobbying activity and "Capitol Words" which explores the most popular words and phrases used by legislators in the U.S. Congress.