Does anyone have any ideas on what is the best polish or cleaner to use on anodized parts such as rims, cranks, etc.? Is there a worry of taking the finish off when using certain products like aluminum polish or chrome polish?

Thanks

Yes- if you use anything too abrasive you will damage the anodized finish. Use a mild aluminum cleaner/polish like Mother's Mag Wheel polish- it's meant for anodized finishes and doesn't have the abrasive qualities of regular polish.
Clean the parts really well before you polish them so that you don't inadvertantly grind any dirt or grit into the finish. I like Formula 409 or Fantastic for cleaning- they don't leave any residue.