I've used Simichrome, Brasso, and Mothers, and find Mothers is most effective at removing surface grime. Simichrome is great at polishing surfaces that are already clean. I just noticed that Mothers states that they do not recommend using it on chrome, which is unfortunate as I've had great results using it to clean up grubby chrome. Anyone had any negative experiences using Mothers on chrome?

All polishes are a very fine abrasive. Mothers is one of the more aggressive polishes available. If used with high contact pressure it will scratch chrome and provide a nice matte finish. Used with a soft wet rag and gentle pressure is relatively safe. Mothers will rapidly take paint off of raised lettering on stamped or etched data plates.