Hi, I'm currently using Photoshop for creating sprites and animations. It gives me better tools for creating detailed art, and easy workflow to create traditional animations. (I draw/paint and then export every frame of a animated sprite as png and put them together in C2).
I also use Blender3D (free software) for 3D based sprites animation (solids most of the time). Just render every frame as png.
Just like you said, Adobe Illustrator is a good software for vector based artwork, it would be better if C2 accepted SVG files though, same goes for Flash drawing tools.
I'd suggest - if you're intending to do some complex characters, scenarios/levels and animations - the purchase of a tablet (digital drawing pen/device, I don't know how you call it in english, lol) such as the Wacon Intuos, Bamboo or even Cintiq series and Photoshop. Most of the professional artworks out there(even for games) are created with these simple and easy to learn tools.
As an example, here's is the first frame of a running cycle animation of a character I'm working on. Also a scene/level concept I created a while ago, both with photoshop and a tablet.
Hope it helps