For high resolution sprites there are plenty of options, such as Photoshop, GIMP, and Paint.net. These work for pixel art as well, but aren't ideal.
If you're going down that road, my experience is less limited tools wise -- I personally use GIMP, because I'm too lazy to learn anything else -- though Piskel
is pretty good, with good animation tools and support for layers and such.
Inkscape is also good if you want to make some nice, clean vector art -- of course, you'll have to export it to raster files for use in C2, but the idea is that you can export large images which scale well.