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I think ray trace rendering had to be done on the CPU for a long time. But since we have compute shaders in OpenGL 4.3 now, it might be possible to move the computations on the GPU and perform passable real time rendering.

What approaches for GPU based ray tracing are there already? Can it compete with rasterization rendering nowadays?

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Probably the state of the art in GPU raytracing is NVIDIA's Optix middleware (free registration required to download it). I haven't looked into its capabilities or performance in detail, though. – Nathan Reed Mar 28 '13 at 16:14
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You can get more than passable real time rendering. The main problem is that a very high end machine is required. The Octane Renderer is a real time renderer aimed at stand alone rendering (think movies). Theres also the Brigade engine (by the same people) which is not currently public. You can find impressive videos of it running on this blog.

They were at siggraph'12 with this demo (video). As you can see, if the scene and camera are still the image converges very quickly and looks quite impressive, but constant movement causes grain artifacts, presumably from limiting the number of bounces per frame. It isn't competitive with rasterization because of this grain and the hardware requirements, but I think it will only become more viable as video cards get cheaper and more powerful.

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Nvidia's OPTIX library for CUDA is probably about as fancy as it gets for fast GPU rendering. Here is a demo that Pixar recently did showing off the use of full film assets in an unreleased renderer doing real time previews inside of Katana. It uses Optix for the ray tracing (and quite a lot of GPU horsepower) to do very rapid preview rendering with lighting that is quickly nearly on par with actual film renders.

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