ParaView.org
This looks powerful and promising
Gephi.org
This looks powerful and promising
OpenRefine
Formerly Google Refine, looks to be more for cleaning data than presenting it?
JpGraph.net
PHP solution
Qlik.com
Qlik Sense Desktop seems free to use, but Windows only. Some "cloud" alternative too?
Power BI Desktop
Another Windows only tool, by Microsoft
Tableau
Can create story also
Tableau Desktop -- subscription required
Tableau Public -- data is made public
plot.ly
data made public, unless pay subscription
d3js.org
Javascript library
rawgraphs.io
Built on d3.js, produce graphs in browser using copy-paste, without sending data to server
leafletjs.com
javascript, for maps
modestmaps.com
javascript, for maps
carto.com
for maps also, free if data made public
envision.js
does not seem so useful