Is it possible to run CUDA on AMD GPUs?

Nope, you can't use CUDA for that. CUDA is limited to NVIDIA hardware. OpenCL would be the best alternative.

Khronos itself has a list of resources. As does the StreamComputing.eu website. For your AMD specific resources, you might want to have a look at AMD's APP SDK page.

Note that at this time there are several initiatives to translate/cross-compile CUDA to different languages and APIs. One such an example is HIP. Note however that this still does not mean that CUDA runs on AMD GPUs.

You can't use CUDA for GPU Programming as CUDA is supported by NVIDIA devices only. If you want to learn GPU Computing I would suggest you to start CUDA and OpenCL simultaneously. That would be very much beneficial for you.. Talking about CUDA, you can use mCUDA. It doesn't require NVIDIA's GPU..

Yup. :) You can use Hipify to convert CUDA code very easily to HIP code which can be compiled run on both AMD and nVidia hardware pretty good. Here are some links

GPUOpen very cool site by AMD that has tons of tools and software libraries to help with different aspects of GPU computing many of which work on both platforms

HIP Github Repository that shows the process to hipify

HIP GPUOpen Blog

Update 2021: AMD changed the Website Link go to ROCm website

https://rocmdocs.amd.com/en/latest/

You can run NVIDIA® CUDA™ code on Mac, and indeed on OpenCL 1.2 GPUs in general, using Coriander . Disclosure: I'm the author. Example usage:

cocl cuda_sample.cu
./cuda_sample

Result: