Geometry Shaders were introduced on the Microsoft side with DirectX 10.0 through Shader Model 4.0 and in the OpenGL world can be found with the most recent 3.2 release (or earlier using the GL_EXT_geometry_shader4 extension).
Zack's Geometry Shaders support comes in a patch that's over 30,000 lines of code and touches many different parts of the Mesa 3D stack. However, this new support is considered "basically working" (bugs may be aplenty) and the only driver implementing this geometry shading support is the Gallium3D software driver.
Right now it's being decided whether the support for geometry shaders will land in Mesa 7.7 or Mesa 7.8. Mesa 7.6 isn't even out the door yet, so it will still be some months before this initial code is found within most Linux distributions. Zack's mailing list message can be read on mesa3d-dev.