Pencil 2D – An animation software for vector and bitmap graphics. It is free, multi-platform and open source
Pencil 2D (FREE)
Synfig Studio (FREE)
Synfig Studio – A free open-source 2D animation software
After Effects
After Effects is an adobe product and is a very popular motion graphics and visual effects programs. Useful for editing and adding post-effects to animations.
ToonBoom
Toon Boom Animation is the leading supplier of animation software and storyboard software for animation studios and media publishers.
Adobe Animate
Adobe Animate allows you to design interactive animations with cutting-edge drawing tools and publish them to multiple platforms.
Animator's Resource Kit 