Texture Synthesis
Image Analogies from Aaron Hertzmann.
Image-Based Rendering
LightPack, a light field rendering package from Stanford.
Non-Photorealistic Rendering
Huge list of non-photorealistic rendering resources.
Radiosity
RAD radiosity source code.Radiator, another radiosity renderer.
RadiosGL, which uses OpenGL for radiosity.
RADical is another radiosity renderer.
irrEdit is a world editor and radiosity lightmap generator.
Volume Rendering
Volreen is an open source volume renderer.
Volpack, from Stanford.
VolView trial software from Kitware.
Lots of volume rendering software from U. Texas.
RenderMan Compliant Renderers
Pixie, an open-source ray tracing renderer.
jrMan, an open-source REYES renderer.
Aqsis is another open-source renderer.
Ray Tracing
The SunFlow open source ray tracer.
The LuxRender is another open source ray tracer.
The Art of Illusion is a free modelling/rendering/animation package.
The Rayshade public-domain ray tracer.The open-source ray tracer Yafray.
Greg Ward's Radiance renderer.
PBRT, the physically-based ray tracer.
The Toxic renderer.
The POVRAY site.
Archive of issues of the Ray Tracing News, including pointers to public domain ray tracers.
GPU Rendering
The OptiX site, from NVIDIA.
RenderMonkey shader tools.
ShaderMan shader tools for python.
Real-Time Global Illumination code - several programs (some GPU, some CPU).
Some Modeling Packages (NOT renderers! Just to help make stuff.)
Blender is the do-everything (model, animate, render) public domain package.
Wings3D is a subdivision surface modeler.
Silo is another subdivision surface modeler, with a 30 day free trial version.