Peter Schröder taught a course in the fall of 2002 at the California Institute of Technology called Hacking The GPU. The subject matter of the course revolved around general purpose computation. Assignments included stable fluid simulation and mesh smoothing. The course notes page has some useful links.
The MSDN DirectX page is a good starting point for DirectX documentation and tutorials.
NVIDIA’s Developer site contains the NVIDIA Cg SDK and plenty of demos, white papers and presentations to help you program NVIDIA GPUs.
ATI’s Developer site contains lots of reference material, demos, and utilities to aid in programming ATI GPUs.
The 3DLabs Developer Support Site has some documentation on OpenGL (including OpenGL 2.0). Their main developer site requires registration.
Matrox’s developer site has information and SDKs for programming their GPUs.
OpenGL.org is the place to look for OpenGL news, specs, documentation, and other details about OpenGL programming.
CGShaders.org hosts discussion forums for users of Cg. These are a great resource for getting help with Cg. The site also maintains a repository of Cg shaders and host regular shader contests.