Free chart/diagram PC programs?

not too sure about the venn diagramming as its probably somewhat tricky with all the positioning + points of intersection (especially if numerically-based/modelled + not purely visual). i havent seen many programs that do that be it diagramming ones or even illustration software. if anything i would aver that a good bet might be mathematica (see http://mathworld.wolfram.com/VennDiagram.html).

outside of that it could be faked in illustrator or any other vector-based ware fairly well with the benefit of advanced styling + all.

Venn diagrams look like Boolean math. Mostly simple overlaps, usually circles.
You can do that stuff in microsoft word—or if it has to be totally free, Open Office.

see OpenOffice workpage here

you can draw simple circles in numerous programs (ppt, excel, word, etc); however, there is the question of accuracy vs mere representation which lies at the heart of the matter.

Venn Diagram Chart by Andy Pope