nVIDIA: Cg
This is David Luebke's lecture on Cg (U of Virginia).
nVIDIA FX Composer Shaders
OpenGL: GLSL
HLSL
nVIDIA: CUDA
AMD/ATI: CAL [Compute Abstract Layer]
Brook, BrookGPU
Stanford: Sequoia
Two companies that are trying to provide middleware:
RapidMind
PeakStream [now part of Google]