If you are using mineral spirits or kerosene, please handle it so as to keep the stuff out of the environment. It is eminently reusable, as several posters have mentioned. No excuse for letting it just drip onto the grass or into the storm sewers. Also remember that mineral spirits are not easily ignitable by themselves, e.g., spilled on the garage floor, but cloths soaked with them definitely are.
I'm in the camp that avoids cleaning chains. By not over-lubing, the chain stays clean enough for me -- no great blobs of oily black steel dust gooping off it. My chains (and my fingers) look just like @
cyccommute's. The mating surfaces of the teeth of the sprockets and chainrings don't get dirty, either. Every once in a great while I use a tiny screwdriver to gently scrape the packed-on stuff off the derailer pulleys -- there really isn't that much, ever, and it's more for show, really -- and it's kind of cool to confirm with a magnet that there is indeed steel in the little chunks that fall off.