Great Software for Plane Geometry
Spirograph

GeoGebra

GeoGebra is a interactive geometry software. Written by Markus Hohenwarter, started in 2001.
For some sample files of GeoGebra, see deltoid curve, cross curve, nephroid curve .
See also: Visual Dictionary of Special Plane Curves
Geometry Expressions

Cabri II Plus
Cabri II Plus, developed in France. Cabri is one of the early interactive geometry software in the mid 1990s. Cabri has a hardware TI calculator version. A particular feature that is first done by Cabri is that it has conics sections as a primitive. That is, you can have 5 points that defines a conic section, that is any of parabola, ellipse, hyperbola. Dragging any of the points will change the conics section. Any other figures build on the conic section will of course change accordingly. This makes Cabri a excellent choice for doing projective geometry.