I've always been fascinated with animation and these days there are loads of professional software tools around that allow you to become a cartoonist yourself.
Pencil tool is a little different from the likes of Flash or Director in two ways: a) it is based around traditional hand-drawn animation techniques, and b) it's free. At the center of the application is a timeline, which allows you to add four types of layers: bitmap image, vector image, sound, and camera. The animation basically works by setting keyframes one each layer and arranging the different layers on top of each other.
You start by sketching out your characters in bitmap format using the pencil tool, before adding a vector layer and inking it out with the pen tool and fill tool. The principle is very simple and the interface is much clearer than that of Flash or a similar high-end animation tool. What I liked about Pencil is that all the tools and options are on display from the start and nothing is hidden, plus you can detach or remove palettes to make things easier on yourself.
The problem with Pencil is that it's very difficult to produce good quality drawings unless you have a graphics tablet - most mouses simply aren't conducive to precise sketching. What's more, there aren't any predefined shapes, objects or templates included that might help you get started. So, while this might be a good way to learn the basic principles of cartoon animation, it's difficult to create anything truly impressive unless you've lots of patience.