This is an older study, but very important. We have more and more people taking male fertility supplements, most of them high in zinc. Yes, zinc will help your sperm quality if you need it. In other words, if you are deficient in zinc it will be beneficial. If your zinc levels are normal, then you may actually damage your sperm. In this study they found that elevated levels of zinc in seminal plasma may be related with defective motility. In other words, unless you have certain physical signs of a nutrient deficiency, you should get tested before deciding which supplements are appropriate for you.
  
Andrologia. 1990 May-Jun;22(3):279-83