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!)
Grease Pencil
Rough Animator
Rough Animator is a fully featured hand drawn animation application that runs on Android, iOS, Mac OS, and Windows. Currently available for $4.99
Storyboarder
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.
Akeytsu
Akeytsu is a piece of 3D animation software and is a lighter, faster and cheaper alternative to Maya. It also has a free educational version.
Krita
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
Live2D has a bunch of software that allows 2D artists to create animations from their artwork. Available in both FREE and PRO versions.
MakeHuman (FREE)
MakeHuman is a free open-source software that allows you to create and pose 3D human characters. Useful for pose reference.
Dragonframe
Dragonframe is the stop motion animation software that captured Laika’s ParaNorman, The BoxTrolls and Disney’s Frankenweenie. Free Trial available.
OpenToonz (FREE)
OpenToonz is a free open-source software for producing 2D animation and is known for being used by Studio Ghibli
Animator's Resource Kit 