Common primary sources of saturated fats in the diet include red meat, full-fat dairy products, and certain plant oils, such as palm and coconut oil. These sources can raise cholesterol levels and increase the risk of heart disease when consumed in excess. It's important to balance saturated fat intake with healthier options, such as monounsaturated and polyunsaturated fats, found in foods like nuts, seeds, avocados, and fatty fish, to promote overall cardiovascular health.