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Depends on what you want to do.

If you want to render fractals using the CPU, C is perfectly fine. OpenGL will not help you there at all, since everything is done on the CPU. This is the approach taken by Mandelbulb 3D, and Mandelbulber.

But if you want to render using the GPU, you can use the flexibility of OpenGL shaders and the GLSL language. Instead of using the traditional OpenGL pipeline, you render a single fullscreen quad using a custom pixel shader, which is invoked for each pixel. The most difficult part is getting the setup right - after that GLSL is very easy to work with - like C, but with support for matrices and vectors builtin. This is the approach taken by Boxplorer, Fragmentarium, fractal.io, and most other GPU renderers.

Both methods have their pros and cons. GPU will be faster (for reasonable graphic cards), but less flexible: some effects cannot be done on an individual pixel basis (e.g. the post-processed Depth-Of-Field used in Mandelbulber requires sorting), and I doubt you can find a GPU with GLSL support for double precision floats.

OpenCL would be more flexible that OpenGL and GLSL, but is much more complicated to setup.

Intel has a web site with the details which features they support in their OpenCL SDK and which they don't.

http://software.intel.com/en-us/articles/opencl-sdk/

One of the major issues would be operating system support. They only support 64 bit Linux (and that support is Beta).

Thanks for clarifying that, I didn't think about performing the actual calculation in GLSL.

Check out "Boxplorer" on Google Code. (c and opengl) It was put together by some people at this forum. I have used the code as a sanity check for my own programming. There is also a Boxplorer2 with added features like DOF etc.

I made boxplorer2 buildable with g++ on linux, the free vc++ on windows and xcode on the mac using some very simple makefiles.
Thanks to SDL abstraction, mostly. See http://code.google.com/p/boxplorer2/source/browse/#svn%2Ftrunk

The particular c++ compiler really isn't that relevant; the cycle burning glsl code gets compiled by the graphics driver, on the fly.