Most people don't need supplementation and can get all the essential vitamins through their diet. 

However, there are many situations when you may consider supplementation:

1. You may be getting some nutrients through your diet, but not the recommended daily amount.
2. You may be on a restricted diet (keto, vegetarian, etc) and thus may in fact need supplementation for certain vitamins, mineral and amino acids.
3. There is a lot of talk about getting vitamins though a regular diet, but what about minerals? Many 'regular' diets can be suboptimal for certain minerals.

Here are some supplements that may help support your immune system:

1. Zinc: While Zinc may not definitely prevent illness, many studies show that supplementation with Zinc can reduce the duration and severity of the common cold, particularly if taken within 24 hours from the onset of symptoms.1
2. Vitamin C: Studies suggest that regular supplementation with Vitamin C may prevent the common cold in people who are exposed to cold temperatures  or extreme physical exertion.2 
3. Elderberry: A powerful antioxidant! A study of 312 air travelers taking daily Elderberry extract found that those who got did get sick had a shorter duration of illness and less severe symptoms than those who do not.3
4. Grape Seed: Grape seed is high in Vitamin E, an antioxidant which protects the body's cells from harmful free radicals.

References:

1. https://www.cochranelibrary.com/cdsr/doi/10.1002/14651858.CD001364.pub3/full
2. https://www.cochranelibrary.com/cdsr/doi/10.1002/14651858.CD000980.pub4/full?highlightAbstract=vitamin%7Cc
3. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4848651/