It fights well against rust stains, tarnish, mineral deposits, soap scum, and indoor or outdoor grime and works on stainless steel, brass, bronze, copper alloys, aluminum, ceramic, porcelain, glass, and Corian.
Check out this BuzzFeeder's review for more on this product.
Promising review: "I was so bummed when I scratched up my pretty white sink with pots and pans. I thought I'd need to have it replaced or try to sand it and refinish it somehow, but I bought this stuff as a last ditch effort to fix it myself. It takes some elbow grease to make them go away, the scratches don't just wipe off, but if you scrub at them for a few minutes they melt away pretty quickly. After two rounds my sink looks nearly brand new again!" —Dan Borden
Get it from Amazon for $9.49 (available in three sizes).