Grease Pencil is a feature inside Blender that allows you to animate in 2D while taking advantage of a full 3D suite of features. Definitely one of the best pieces of software that blends the two together so seamlessly (and free!)
Storyboarder is a free open-source piece of storyboarding software that makes it easy to visualize a story as fast you can draw stick figures.
Krita is a free app for digital painting but also supports 2D animation. It is made by artists that want to see affordable art tools for everyone.
Live2D has a bunch of software that allows 2D artists to create animations from their artwork. Available in both FREE and PRO versions.
MakeHuman is a free open-source software that allows you to create and pose 3D human characters. Useful for pose reference.
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