In a large placebo controlled double blind study of ten year duration published in JAMA it was shown that supplementation with 200mcg of selenium a day can reduce the risk of cancer by 50%.
Supplementation with calcium citrate has been proven to prevent osteoporosis. Any calcium supplementation should also include vitamin D (the calcium absorbtion hormone) and probably magnesium.
Magnesium has been shown to reduce cramps and improve sleep in those suffering from restless legs syndrome.
Magnesium has also been used to prevent brain damage after severe head injuries.
Organic chromium has been proven to decrease stress and lower blood sugar level, and is beneficial for diabetes and insulin resistance.
Zinc is used by over 100 enzymes in the body. Even minor zinc deficiency can cause symptoms.
One study showed that 1200mg a day of coenzyme Q10 can reduce the symptoms of Parkinson's disease by 40% whilst preventing further degeneration.
Antioxidants called bioflavonoids are not strictly speaking vitamins, but their antioxidant activity appears to be highly beneficial. For example several studies have been done suggesting that the bioflavonoids in cocoa can greatly reduce not only the risk of heart disease, but of all deaths.
In one study done on rats it was found that thiamin (a B vitamin) in large doses could combat toxicity induces by too much sugar. In general the whole B group of vitamins represent that which is taken out of refined sugars. The body need the B vitamins to metabolize sugar. Niacin is also depleted with carbohydrate and alcohol intake. In our culture dementia starts at age 45 and increases with age. One study showed that vitamin B3 (niacin) can actually stop the progress of dementia.
Vitamin C is required for collagen production and beautiful skin. Vitamin C in an antioxidant which can prevent aging by fighting free radical damage.