Generally speaking, there isn't much need for supplementation, when the individual in question is healthy, eating proper food, and doesn't suffer from past malnourishment. Quite to the contrary, I've found the need for supplementation often speaks to an inadequate or improper diet.
There seems to be a notable exception in vitamin D. Differently to other vitamins, vitamin D3 is primarily produced by our bodies with the help of sunlight and not ingested with food.
The further up north or down south you live, the less sunlight you'll be exposed to during the winter. This depletion of vitamin D during the winter season probably lends an explanation for the seasonality of the common flu or cold, for vitamin D3 is highly important in the proper function and regulation of our immune system (Mora et al. 2008).
We could of course every winter migrate away from shortened daylight toward the tropics, as many birds do, but I think you'll agree, that this is hardly feasible. But even around the equator or in summer we can easily fall into vitamin D3 deficiency simply due to our primarily indoor lifestyle.
One solution would be to just simply spend more time outside, but this isn't necessarily feasible, if you're working a job indoors. You can't just dip for two hours to go fuel up on sun. Thus, the simplest solution seems to me to just supplement vitamin D3.
To this end, I tend to supplement 7,000 IU every one to three days and have had good results with that (no illness to speak of) and no negative side effects.
References
Mora, J.R., Iwata, M., and von Andrian, U.H. (2008). Vitamin effects on the immune system: vitamins A and D take centre stage. Nature Reviews Immunology 8, 685-698. 10.1038/nri2378.
