That's actually a very interesting one, and has been written about at length by a number of medical stats people.
Hopefully I do them justice to their arguments by saying that the benefits from supplements (if any) are tiny - as in a hazard ratio of death is pretty much 1 unless you are actually deficient. Equally however the potential downside of them is pretty much zero - expensive wee is what they can mostly be summarised as. Whilst they may be money wasted, the're mostly benign, save the odd tragic case.
If supplements had the side effects of chemotherapies however, they'd be banned straight away - without evidence of benefit, the risks would be too high.
No, you do not. Just look at the market of dietary supplements.