The cartoon animation software listed in this page are vector based.
Unlike the Classic Animation Software that are designed for drawing animation frame by frame, a vector based software lets you use the computer to do some of the hard work.
Flash animation is a popular example of this genre. It is not, however, a dedicated animation software, but a web-authoring tool. It does lack in - how shall I call it - "animation mentality".
ToonBoom recognized this and came up with an entire family of animation software that export SWF but are actually designed with making animation in mind.
It's up to you to know what you need.
Both have a trial period, so you can see what works best for you.
Also listed below are a number of completely free cartoon animation software.
As with all free software, they vary in complexity and the features that they provide.
If you've never worked with symbols and "tweens" before, you might need a little practice to get the idea behind this technique. Do browse the Flash cut out animation tutorials in this site to get an impression of how it's done.
It might be better to get the hang of it with a free software, before investing a couple of hundred dollars in a big professional program.
Aniboom's ShapeShifter is a great place to start.
Be careful - it's addicting :-)
I started out as a classic animator, and didn't even want to look at cut outs, but once I started I got hooked on the marvelous things you can do with symbols.
You can always use these software to create or draw animation frame by frame -
But you can't use Symbols in a Classic animation software. (TVPaint is the only exception, I think).
So if you're just starting to learn animation, leave your options open.
A little peak into the Flash spirit... speaking from the GUTS, I'm sure you know this one, but I though I'd put it here anyway:
A whole family of programs for making animation, for all levels of animators, from kids to pro:
An online animation widget from aniboom.com, quite simple to use and a great way to make a first try with object (symbol) animation.
Create your animation, export it as GIF animation, and mail to your friends.
Sooo many people have discovered this software and go crazy with it.
Just search YouTube for "stickfigure animation" and see for yourself...