Contrary to what some sources claim, how much antioxidants there are in star anise (Illicium verum) is far from impressive for a spice. Compare its ORAC value to ground cloves (290,283) or even your basic black pepper (34,053) and you realize where it truly ranks. This is augmented by the fact that star anise is used even more sparingly than your average spice, and hence, you are consuming only minuscule quantities of it.
While popular in its native growing region of China and Vietnam, its bitter licorice flavor has yet to catch on in the United States. Perhaps that's a good thing, as there are much healthier (and cheaper) choices for you to spice up your dishes with.
Research Support, Non-U.S. Gov't: Carlsen MH, Halvorsen BL, Holte K, et al. Nutrition Journal NIH Jan 2010