http://www.inkscape.org (Vector art program. Relatively simple. This is good for creating really clean-looking geometric art or linework, but not for coloring sophisticated things like in Photoshop.)
http://www.gimp.org/ (Raster art program. This is a lot like Photoshop. Good for coloring or photo-editing.)
That's what I'd recommend to you! Those are both free. PM me if you want to know more!
If you're willing to torrent or shell out some cash, Adobe Illustrator and Adobe Photoshop are tops.