Open Source Animation Software
Blender
Blender is a free and open-source 3D model software released under the GNU General Public License. The software can be used for 3D modeling, 3D animation, UV unwrapping, texturing, rigging, skinning, rendering, particle generation, water simulation and much more.
Synfig Studio
Synfig Studio is a free and open-source 2D animation software for Windows, Linux and OSX.
Pencil2D
Pencil2D is a simple, yet powerful 2D animation, drawing and painting application that lets you create traditional hand-drawn animation using both bitmap and vector graphics. Pencil2D is released as free and open-source software under the GNU General Public License and uses the Qt framework. With Pencil2D you can seamlessly switch between raster and vector workflows, allowing you to sketch, ink & paint on the go.