Useful programs for data analysis and demonstration

Octave

A free version of Matlab, very easy to handle massive amount of dataset.
Official Wiki Examples

Xmgrace

Interactive plot program, output nice postscript format.
Official Wiki

Gnuplot

A powerful program for plotting and for fitting simple functions. If the plot is simply a 2D curve, I prefer to use Xmgrace. For fancy stuff, Gunplot is extremely good!
Official Wiki Examples FAQ

NMR packages

NMRPipe and NMRdraw

Official

SPARKY

Official