If you often eat fatty cuts of meat, your intake of saturated fat and cholesterol is likely too high. That means you are at greater risk for high cholesterol, heart disease, and stroke. Animal fats provide about 2/3 of the saturated fat in the American diet. Foods that are high in saturated fat tend to be high in cholesterol, too. Organ meats, such as liver, kidney, sweetbreads, and brains, are very high in cholesterol.