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Plotting

These programs all perform two-dimensional plots. Most also do some plots of three-dimensional data. They have strengths for various disciplines, so you have to investigate their websites.

Free

Gnuplot - Linux, Windows
Gnuplot is a very quick scriptable plotter with a command-line interface. It's a fine workhorse that is easy to connect to from external programs, but the resulting graphs are not print-quality. It does 2D and 3D graphs.
Grace - Linux, Windows
The interface to this program is a little confounding at first, but its 2D plots are print-quality, so everyone uses it. Under Windows, it runs only through X-Windows, so you would need Exceed or some such to run them.

Commercial

SigmaPlot by Systat Software  - Windows
The 2D plots from this program are lovely. It has a Windows COM interface so you can call it from a Windows program.
Origin by OriginLab - Windows
To get COM integration, you must upgrade to OriginPro.
Tecplot by Tecplot, Inc.  - Linux, Windows, CTC
It has add-ons that enhance visualizations of higher-dimensional data.
DeltaGraph by Red Rock Software  - Windows, Mac
This is probably the simplest plotting package.
Igor Pro by WaveMetrics - Windows, Mac
This has always been known for having a natural language interface.

These programs all perform two-dimensional plots. Most also do some plots of three-dimensional data. They have strengths for various disciplines, so you have to investigate their websites.

Free

Gnuplot - Linux, Windows
Gnuplot is a very quick scriptable plotter with a command-line interface. It's a fine workhorse that is easy to connect to from external programs, but the resulting graphs are not print-quality. It does 2D and 3D graphs.
Grace - Linux, Windows
The interface to this program is a little confounding at first, but its 2D plots are print-quality, so everyone uses it. Under Windows, it runs only through X-Windows, so you would need Exceed or some such to run them.

Commercial

SigmaPlot by Systat Software  - Windows
The 2D plots from this program are lovely. It has a Windows COM interface so you can call it from a Windows program.
Origin by OriginLab - Windows
To get COM integration, you must upgrade to OriginPro.
Tecplot by Tecplot, Inc.  - Linux, Windows, CTC
It has add-ons that enhance visualizations of higher-dimensional data.
DeltaGraph by Red Rock Software  - Windows, Mac
This is probably the simplest plotting package.
Igor Pro by WaveMetrics - Windows, Mac
This has always been known for having a natural language interface.