For many years we used Gnuplot exclusively, but we needed something simpler for younger, less experienced co-authors, so we've gravitated toward graph.exe.
We do a lot of analysis in the OpenOffice spreadsheet, Calc, I think. Some of the graphs are done in there, a few co-authors have learned to customize and make things really nice.
There's a program called Scidavis that is easier to use than Gnuplot, but also gives the parameter uncertainties for least squares fitting.
We roll our own Fourier analysis code.