Krita: free software for digital painting and animation.
Blender is a professional free and open-source 3D computer graphics software product used for creating animated films, visual effects, art, 3D printed models, interactive 3D applications and video games.
OpenToonz is a powerful, full animation package that was recently released as open source (free).
Processing is an open source programming language and environment for people who want to program images, animation, and interactions.
USEFUL LINKS FOR BLENDER:
Blender.org: the home page for the software
BlenderNation: news, tutorials
Blender Artists: Blender artists community
Blender on Reddit: new, tips, hints
Blender 3d Content Creation: N00b to Pro: useful free WikiBook
Blender Cookie: tutorials covering many aspects of Blender; some free
The 33 Best free Blender Tutorials: list of tutorials on the web
Tufts University Blender 3d Design Course: lots of good tutorials
Blender Guru: tutorials
USEFUL LINKS FOR OPENTOONZ:
OpenToonz user forum in english.
USEFUL LINKS FOR PROCESSING:
Processing.org: homepage of the program.
Hello Processing: interactive beginner lesson created for the Hour Of Code.
Experiments in Processing: list of tutorials and resources.
Open Processing: a place to view and share processing sketches.
Sketchpad: online Processing integrated development environment
2D ANIMATION SOFTWARE:
Pencil 2d: open-source animation program: Free for most operating system.
Digicel Flipbook: traditional animation program: widely used in the industry.
Toon Boom Software: has a whole range of 2d animation software; widely used in the industry.
TV Paint: another popular 2d animation program.
Clip Studio Paint EX: well-regarded 2d art and animation program.
Rough Animator: Powerful 2d animation software for iOS, Android, Windows and Mac OSX.
3D PRINTING RESOURCES:
Makerbot: resources for the Makerbot 3d printer.
Thingverse: a design community for discovering, making, and sharing 3D printable things.
OTHER USEFUL SOFTWARE:
GiMP: free, open-source advanced imaging program, available for most operating systems.
Inkscape: powerful, free and open-source vector graphics editor, available for most operating systems.
Kerkythea: free multi-platform software for 3d rendering.
Audacity: open-source, cross-platform audio editor.
WINGS 3D: free advanced subdivision modeler, available for most operating systems.