The Blender Foundation maintains the most popular, free, open-source 3D suite, Blender. One major component of any 3D application is the chunk that turns 3D geometry into one or more 2D images. This is often passed to third-party software, like mental ray or Pixar Renderman, but basically everyone has their own internal ones.

About five years ago, Blender released a new rendering engine, called Cycles, whose just-released 2016 demo reel is embedded above. Not being held back by history, they swung for the fences with it. It supports multiple GPUs (albeit mostly NVIDIA, even to this day, due to CUDA vs OpenCL at the time — but AMD might be commissioning development soon) and integrates tightly with the editor. It produces great images, although it's very slow for cartoonish imagery (but Blender is working on a viewport renderer for that sort of content anyway).

Also, Blender with Cycles is what we used for our recent animation projects. Version 2.78 is currently in release candidate mode, and should be released very soon.