OpenToonz is a free open-source software for producing 2D animation and is known for being used by Studio Ghibli
Source Filmmaker is a free movie-making tool built and used by Valve to make movies inside the Source game engine. It is a full package and can be used to make cinematics using Valve models and environments.
Kinovea is video player that allows you to slow down, study, draw and comment. Primarily made for sports enthusiasts but useful for animators too.
Animation Paper is a popular free software for hand-drawn animation created by Niels Krogh Mortensen
Daz 3D – A 3D morphing, posing, animation and rendering suite, normally retailing at $249 but is now free to download
Pencil 2D – An animation software for vector and bitmap graphics. It is free, multi-platform and open source
Synfig Studio – A free open-source 2D animation software
Blender is a free open source 3D modeling, animation, video editing & compositing software. Like Maya but FREE!