For some soups you will need to use a perfectly clear broth. Oddly enough, white broth—if it’s made with bones—will stay cloudy no matter how carefully you skim it and keep it at a slow simmer. If you need a clear broth, make a brown broth or a white broth made from whole chicken parts with the skin removed.
Even brown broth that is carefully skimmed and prevented from boiling will remain slightly cloudy because of minute particles of protein that get stirred up when you strain it. The only way to eliminate these particles is to strain the broth through a triple layer of cheesecloth or a cloth napkin. Any broth, white or brown, can of course be clarified with egg whites, but I always avoid this extra step if I can.