Very few people have "normal" skin and can get away without using moisturizer. If you're regularly washing your face — even just with water — you should be moisturizing too. If you have oily skin, skipping moisturizer won't prevent acne and will lead to premature signs of aging. If you have dry skin, skipping moisturizer will result in skin cracking, itching, flaking, and becoming tight and red. If you have sensitive skin, skipping moisturizer leaves skin susceptible to environmental irritants.