Stains in kitchen sink

X2 on Bar Keepers Friend, and a Scotch Brite scrubber. Works on all surfaces, and doesn't scratch.

How about Oxiclean and a brush?

I know some of you will poo-poo this idea, but before I started installing granite in my new homes, I used a lot of solid surface product. When we were doing the final cleaning for the new homes we often found stains and scratches in the solid surface. I asked my installer how to remove the stains and scratches, he said; "Use sandpaper, the wet or dry type for auto body use. Add a little water while you sand and all will be well". I tried this trick a few times and it worked great. Now, if your sink is not solid surface and plastic, then this method may not work. But, I remember using about a 400 grit paper, and I don't think that would hurt a plastic sink. I haven't used solid surface in about 10 years, so no recent experience, but it did work in the past.