Plastic Animation Paper is a powerful and professional 2D animation package, once sold commercially for 695 Euros, now available for free.
The program allows you to draw directly to the screen (in video or film resolution) using a tablet. Although if you don't have one then it'll work with a mouse, too.
The light table then allows you to see several layers of drawings while you flip through them in real time to see the animation effect. Cutouts speed the animation process by allowing you to create a library of scenes, characters and effects that you can reuse later. You can even import and work with a soundtrack to ensure that your work is perfectly synchronised.
If you're just looking to create the very simplest of animations - a bouncing ball GIF for your website, say - then Plastic Animation Paper isn't for you. It's a huge program with a quirky interface that ignores all the usual Windows conventions: just finding your way around will take quite some time.
If you're an artist who would like to turn your work into a polished and professional cartoon (for instance), though, this program can help you to make it happen. Just be sure you check out the tutorials, which will explain how everything works.