In my quest for shiny shower heads and faucets, I have purchased a bottle of Bar Keepers Friend Liquid Cleanser. I could not find any product designed specifically to clean faucets and shower heads, but I thought this one should work after I'd read that it can be used on stainless steel, among other things (glass, tile, ceramic, porcelain, fiberglass, cultured marble).
The cleanser contains citric acid and is said to work without much effort applied; gentle rubbing should be enough. However, when cleaning faucets, I found myself having to use some strength, often reapplying more of the product to achieve the desired results. The sparkling clean look I wanted does not come easy and unfortunately does not last. Bar Keepers Friend works better on tile and glass, but for metal, I will have to find something better.