If you are about to invest some serious time into learning an application, may I suggest Blender 3D?
You can make animated sprites really fast.
By learning different rendering and material combos you can do everything from Pixelated retro graphics, to photo realistic graphics. Look into "Toon" rendering, Photoreal rendering, and retro rendering.Another great medium that is nearly impossible to freehand draw is Isometric tiles. Blender makes it really easy!
It also imports from other applications so you can use things like Make human to make you characters :
http://www.makehuman.org/
(caution, it makes naked people, just like god does.)
Another nice application is Zbrush but it is quite costly.
Another route in to use Synfig. This is how Anime and all the other japan cartoons are made.
Blender is a lot faster to learn than synfyg. Blender makes it really easy to get the shading you want.
For nifty backgrounds try Vue De Espirit. It generates trees and all kinds of other goodies for you. Can also make neat fly around animations for your cut-scenes or whatever.
Have fun <img src="{SMILIES_PATH}/icon_e_biggrin.gif" alt=":D" title="Very Happy">