Synfig Studio is a free cross-platform 2D animation software that allows users to create quality 2D graphics using bitmap or vector images. The program has some similarities with the Gimp which some users will quickly familiarize themselves with this program.
To install Synfig Studio on Ubuntu (32-bit & 64-bit), then download and install the appropriate deb package from one of these two links:
Here is an animation created by this software:
For more details about this software, check their website here.