Many cosmetics contain ingredients that can irritate or dry the skin if left on for too long. The best thing you can do for your skin is to find a good cleanser and use it every night.
When choosing a cleanser, make sure to choose the right one for your skin type. For instance, if you dry skin use a gentle cleansing oil and if you have oily skin try using a foaming cleanser. For sensitive areas such as the eyes, use a gentle makeup remover.
Keep in mind that waterproof mascaras tend to be more stubborn, so special eye makeup remover may be needed. As any cleansing ritual, apply moisturizer afterwards to keep your skin healthy and hydrated.