There are dozens and dozens of antioxidants, vitamins, and minerals that can contribute to optimal health. Just as a few examples ...
Vitamin B1, for example, is used in many chemical reactions in the body and is present in every tissue. It helps convert glucose to energy. Deficiency can create neuromuscular, gastrointestinal, and cardiovascular problems.
This is incapable of being produced by the body, and must be present in the diet. Unfortunately, it is one of the most common nutritional deficiencies in humans - a US Dept of Agriculture study reported that 45 percent of Americans consume less than the USRDA.
Calcium is an example of a mineral. It is the most abundant mineral in the body. Beyond bones, calcium affects how nutrients pass through cell walls, is used in muscular contraction and even helps cells bind to each other. The epidemic of Osteoporosis is evidence enough that people are not receiving enough calcium. The Western diet, which is high in saturated fats, salts, animal proteins, and processed sugars creates acidic waste products. This means the body must leech calcium from the bones to form an alkaline environment. Most people mistakenly take on dairy for calcium, not realizing that plants are a more abundant source and dairy actually increases the body's need for calcium, so it's a catch-22.
Those are examples using two sample vitamins and minerals. There are other antioxidants, such as CoQ10, that have been shown to improve cardiovascular health, etc. The issue is that our environment is much more toxic than it was even 100 years ago. Not only do crops yield fewer nutrients, but our body REQUIRES more to combat contaminants in the air, in the soil, in the water supply, and even to combat the stress that we cause in our jobs and fast-paced lifestyle.
Most people try to rationalize their vitamin intake by deciding that they will see if they "feel" a difference and then choose whether to continue or not. The fact is that degenerative disease is an epidemic. According to the Journal of the American Medical Association, the second leading cause of death in the year 2000 was lack of exercise and poor diet (not lack of calories, either, Americans over consume calories but are malnourished because the food supply is so processed that vital nutrients are damaged or removed and unavailable). People don't "feel" their arteries clogging even though a large number of adolescents and even young children suffer from atherosclerosis due to the poor diet and toxic environment we live in.