Last June the answer was a qualified no: Can I use the GPU for calculations?
However, the Videocore driver code was open sourced towards the end of 2012: http://www.raspberrypi.org/archives/2221 - does that mean we're now likely to see it happen?
If so, given existing libraries (http://mathema.tician.de/software/pyopencl, http://www.jocl.org/) might already work, but with a CPU implementation, it would seem reasonable to start using them in the hope they'll soon be able to use the GPU.
OpenMAX is supported. It does not let you do arbitrary computations on the GPU, but it seems to contain compression and decompression of audio, video and images. This thread is about JPEG decompression with OpenMAX on the Pi.
Here is a list of API:s supported by the VideoCore.
The situtation dramatically changed in 2014 with the official release of documentation on the QPU units in the Pi GPU. The blog featured several GPGPU projects after that. Since then , the number of Pi GPGPU projects has risen.
See for example "GPGPU python library for the Raspberry Pi" : https://github.com/nineties/py-videocore
