Beta carotene as a component of food prevents cancer, but when given as a supplement to help prevent lung cancer in smokers the rates of lung cancer actually increased. Not just one study but a meta-analysis of four.
A healthy diet full of fresh fruit and vegetables appears to prevent cancer but this study found an increased risk of melanoma - the scary fatal skin cancer - with vitamin supplementation.
From a 2008 Cochrane Review of all the available literature: "We found no evidence to support antioxidant supplements for primary or secondary prevention. Vitamin A, beta-carotene, and vitamin E may increase mortality." That means people taking these latter three supplements were actually more likely to die than those who were not.
I don't take any pills from little plastic bottles that I don't absolutely have to take - medicines, vitamins, nutrients, etc. I give my body good nutrition, adequate exercise, and a little sunlight every day. I support it's ability to detox and thereby prevent cancer and chronic disease by making sure it has all that it needs in a natural way.
I don't consider any whole food a "supplement." I eats tons of fresh fruits and veggies, lots of fiber, an occasional egg to get B12, and I expose myself to sunshine to get vitamin D. I stay away from meat and milk and only rarely eat a little cheese. There's almost always 2 tablespoons of flaxseed in the first meal of the day. I eat chia seed pudding or add the seeds to vegan baked goods or other meals.
When I get an upper respiratory virus, particularly a sore throat - which is rare - I may suck on some zinc lozenges for the first 24 hours to effect speedier recovery. Taking zinc every day all the time interferes with copper absorption which can lead to a neurological clinical syndrome of lower extremity weakness, balance problems, etc.
When I have bowel problems that aren't resolving - IBS-like symptoms - I either eat live cultured yogurt for a few days or, if particularly severe, I take a probiotic.
The supplement industry is a 24 billion dollar a year machine that wants your money. Taking something every day that you don't need and that hasn't been adequately proven to help - and might even harm - makes little sense for anyone except the people who stand to benefit financially. I don't like to be a sucker and to waste my cash - and that means avoiding "manufactured" nutrients - except for on the rare occasion when I am ill and feel a little boost has substantial benefit. Better that than a pharmaceutical.
Food is medicine. Just eat right.
For anyone who absolutely can not eat a healthy diet because of financial or geographic constraints, a good multivitamin may be warranted.