At the Wolfram Technology Conference last week, I gave a talk about how to use Mathematica 6 computational and graphics capabilities to visualize Riemann surfaces.
The results shown were based on the revised for Mathematica versions of Subsection 2.3.7 of the Graphics GuideBook and 1.12.1 of the Numerics GuideBook.
The complete talk with images, animations, and demonstrations can be downloaded from http://library.wolfram.com/infocenter/Conferences/6968/
The new, extended version of the code of 1.12.1 of Numerics has been put together as a package and can be downloaded from http://www.mathematicaguidebooks.org/V6/downloads/RiemannSurfacePlot3D.m