Perhaps the most well-known nutrient when we think about coughs, colds, and immune function. It has long been known that extreme deficiency can cause scurvy, but what is maybe less well known is that vitamin C is required for collagen production. Collagen is one of the proteins responsible for maintaining the barriers to external pathogens. If the barrier is impaired, you increase your susceptibility to infectious pathogens.
There is also a vicious circle. Vitamin C is needed by our white blood cells. So, if we become ill, we deplete our own stores of vitamin C, and then become more susceptible to illness again. Vitamin C has not always been found to reduce or risk of becoming ill but has been shown to reduce how long we are ill for, as well as the severity of the symptoms that present. 100-200mg per day has been shown to be a reasonably prophylactic dose.
If you increase your vitamin C intake to 1000-2000 mg per day, studies have shown that this reduces the duration of symptoms by around 20%.