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