My favorite would have to be {c:|x[n]|<inf:x->x^2+c} (Don't know if that's the official way to state the graph) as a function of c in the complex plane. Well, I guess that doesn't count as any of those 3...
My favorite polar graph is
r=20tan(20theta)
It looks like that geometry thing where there's a many sided polygon and you connect all the vertices and there are a lot of these polygons nested within each other... well you'd have to graph it to see what I mean.
What are your favorite cartesian, polar, or parametric graphs?