Graphing Software
last updated 10/17/12
General Purpose

A 2d grapher that is easy to use.  That is one of the main reasons I like it.  It supports explicit, parametric, and polar equations.  It can also plot a list of points.  In addition, it has support for shading (useful for inequalities or area under the curve). It also has some built in calculus functions like being able to find length of a curve or area under a curve. 
Graph Screenshot

An easy to use 2d/3d grapher.  For 2d graphing, it can do explicit, parametric, or polar For 3d graphing, it only does functions of two variables, either Euclidean or polar.  The ease and 'prettiness' of the graphs is the main draw.  I love being able to rotate the 3d graphs with my mouse and I love having a fully shaded surface rather than just a wire mesh.  I also appreciate the speed and responsiveness of the program.  Despite last being updated in 2004, it runs very well on modern PCs.
Graph Calc

This is one of the more powerful free graphers that I've come across, but it is also one of the most cumbersome to use.  It can graph the widest array of 2d/3d graphs I've seen (explicit, implicit, parametric, polar, and spherical).  But be warned, it has a steep learning curve.  Even something like rotating a 3d figure is non-intuitive.  You have to use the keyboard; you can't just drag with a mouse.  While not horrible, it's little things like this that make it difficult.  However, if you take the time to learn it, it is quite powerful and has the potential to produce very nice looking graphs.
Winplot Screen