The Academy of Nutrition and Dietetics and the United States Department of Agriculture, along with other experts, suggest we keep our saturated fat intake to no more than 10% of your daily calories (your total fat intake should supply around 20 to 35% of your calories). For a person who consumes 2,000 calories per day, that would be about 22 grams of saturated fat, which is the amount of saturated fat found in four ounces of cheddar cheese, two cups of ice cream, or two large cheeseburgers. Some diets, such as the DASH diet, reduce that recommended amount even further (to about 7% of your calories); however, there doesn't appear to be any evidence that reducing your saturated fat intake to less than that amount (or eliminating it all together) would be any more or less beneficial.
If you usually eat more than the recommended 10% of your calories from saturated fat, it's probably worth the effort to reduce your saturated fat intake to that level, especially if you have problems with cholesterol or high blood pressure. But that's only part of your dietary plan for reducing your cardiovascular risk -- you need to replace those saturated fats with healthy foods and reduce your total calorie intake if you are overweight or obese.
Eating too much saturated fat appears to elevate your levels of LDL cholesterol (the bad kind) and may lead to a pro-inflammatory state, both of which increase your risk of cardiovascular disease. Reducing the excess saturated fats should reduce those risks, but that may not happen if you replace the saturated fats with refined carbohydrates (white bread, pasta, sugar, high fructose corn syrup, etc).
However, if you replace the excess saturated fats with polyunsaturated or monounsaturated fats (the good fats found in fish, nuts, seeds, legumes, canola and olive oils), you probably will reduce your risk of cardiovascular disease because the good fats reduce elevated LDL cholesterol levels and reduce inflammation. Increasing your intake of polyunsaturated fats may also help to reduce elevated blood pressure; however, those good fats don't appear to have much of an affect on insulin sensitivity, which is a risk factor for both cardiovascular disease and diabetes.
Don't replace the excess saturated fats with artificial trans-fats. They're often found in stick margarine, shortening, and foods made with partially hydrogenated oils. Trans-fats appear to increase your risk of cardiovascular disease, probably even more than saturated fats.
Your saturated (and total) fat intake is only one part of your diet that effects your heart health. Overweight and obesity are also risk factors for cardiovascular disease -- losing weight may also help to reduce high blood pressure and improve your cholesterol. It's also important to eat a balanced diet that includes lean proteins, healthy fats, plenty of fruits and vegetables, whole grains, and low or non-fat dairy products.
Sources:
Academy of Nutrition and Dietetics Evidence Analysis Library. "What is the relation between LDL-Cholesterol and replacing dietary saturated fatty acids with MUFAs and PUFAs in patients with disorders of lipid metabolism?" Accessed February 1, 2011.
Jebb SA, Lovegrove JA, Griffin BA, Frost GS, Moore CS, Chatfield MD, Bluck LJ, Williams CM, Sanders TA; RISCK Study Group. "Effect of changing the amount and type of fat and carbohydrate on insulin sensitivity and cardiovascular risk: the RISCK (Reading, Imperial, Surrey, Cambridge, and Kings) trial." Am J Clin Nutr. 2010 Oct;92(4):748-58.
Mozaffarian D, Micha R, Wallace S. "Effects on coronary heart disease of increasing polyunsaturated fat in place of saturated fat: a systematic review and meta-analysis of randomized controlled trials." PLoS Med. 2010 Mar 23;7(3):e1000252. Siri-Tarino PW, Sun Q, Hu FB, Krauss RM. "Saturated fat, carbohydrate, and cardiovascular disease." Am J Clin Nutr. 2010 Mar;91(3):502-9.
Walker C, Reamy BV. "Diets for cardiovascular disease prevention: what is the evidence?" Am Fam Physician. 2009 Apr 1;79(7):571-8.


