For animation, I'm drawn to two programs that seem to be very good. My choices are a bit limited since I am only looking at open-source software, and only for Windows, at that.

The first tool that I am very impressed with is Blender. The documentation for the tool itself is pretty weak, but there are many books, tutorials, videos, etc. on the tool.

The other tool that I have been using for hand-drawn animation is called Pencil.

Not that I have created a great deal of animation (yet!), but these two are definitely keeping their place on my computer.