Healthy people produce Coenzyme Q-10 in the body.  For those who are reading this question and are unfamiliar with Coenzyme Q-10, it is a fat-soluble vitamin-like substance present in our body's cells. One of its functions is as an antioxidant. 

Despite what you may have heard through supplement advertising, a very profitable business, mind you, health professionals do not advise supplementing with Coenzyme Q-10. For most healthy people, the major source of Coenzyme Q-10 is that produced in the body.  It is also naturally present in small amounts in a wide variety of foods including organ meats, as well as beef, soy oil, sardines, mackerel, and peanuts.  

Some research has been done examining Coenzyme-Q10 and its role in heart disease and cancer prevention. However, there has been no clear documentation of its beneficial effects, and a large amount of misinformation surrounds the use of this supplement. In addition to a lack of research supporting supplementation with Coenzyme-Q10, adverse reactions to it include anorexia, diarrhea, tissue damage and mild nausea. Considering these adverse effects, more research needs to be done examining Coenzyme Q-10 before making any recommendations for supplementation.

References: 
http://wwwcsi.unian.it/coenzymeQ/treatmen.htm
http://mayoclinic.com/home?id=HB00018