These are examples and resources about renderer:

Ray Tracing:

YafaRay: .

LuxRender: original based on PBRT in 2007.

Physically Based Rendering, Second Edition: From Theory To Implementation by Matt Pharr.

Ray Tracing from the Ground Up by Kevin Suffern.

RenderMan compliant renderers:

Pixar RenderMan(PRman): RiSpec, the RenderMan Interface Specification. It is built around the REYES algorithm. The popular shading language is RSL developed by Pixar. OSL released by Sony is another story(check the OpenImageIO too).

Aqsis: Open source 3D solution adhering to the RenderMan interface standard by Pixar Animation Studios.

Pixie, a bit like a dead project since 2005.

3Delight, 6 months of free license.

From this pic, RenderMan is just an API to communicate with renderers(RenderMan is not a renderer, it is an interface description. But often renderman is used as a synonym for the render PRman itself). There are two main parts of RenderMan: 3D scene description language(.rib, RenderMan Interface Bytestream), and Programable shading language(.sl). Introduction to PRman.