Lipitor is a drug intended to help lower cholesterol. The generic name for this brand-name medication is atorvastatin.What are the side effects of Lipitor (atorvastatin) cholesterol medication?Lipitor has been an effective treatment for many people across the country who suffer from high cholesterol. It lowers your cholesterol and, therefore, lowers your risk of heart attack, heart disease, hardening of the arteries and stroke.Like all prescription medications, Lipitor may cause some side effect.