Calculating Viterbi paths for Hidden Markov Models is faster by an order of magnitude or two than doing it on the CPU. I worked on porting NVIDIAs OpenCL implementation to a more 'platform neutral' version for the research project I'm involved in.
I think the question is about how the kernel can use the GPU. Linux probably doesn't need to train hidden Markov models. It might, however, need to do crypto (e.g., for an encrypted filesystem).
Oh gosh you're right. I wasn't thinking about the context in which the question was posed. Anyway, hopefully someone will find those examples interesting. NVIDIA's CUDA developer zone is chock full of great resources for GPGPU (like video lectures and tools and code examples).
Here are some more examples:
http://developer.download.nvidia.com/compute/opencl/sdk/webs...
There are many, many applications beyond crypto.