Blender--model, render and animate 3D models, dynamic particle systems, video tracking and compositing, photorealistic results, import and export a wide range of model types to and from other software, including Alembic animations and all for free!
If you have the patience for it's steep learning curve, Blender is capable of first-class results, and the active community means thousands of tutorials are just a Youtube search away.
Blender's user interface is frustrating--What other program out there uses the RIGHT-CLICK as the primary selection tool? The interface, besides being confusing, changes with every new version. Being open source, sometimes promised new features arrive years late.
Blender is so powerful and has so many features it's overwhelming. Approach with disclipline. Decide what aspect you want to tackle first (modelling, animation, lighting, compositing, etc...), then work through a lot of Youtube tutorials.
I use Blender for light modelling and for cleaning up problem geometry with downloaded models before importing them into other animation or compositing software. Of course, being free, it's value is, literally, incaluculable.