For many people, foods rich in saturated (eg. fatty red meat, whole-fat dairy products) and trans fats (eg. fried food, commercial cookies/crackers, stick margarine) will raise LDL cholesterol (and/or lower HDL).
Though less harmful than saturated fat, it's a good idea to also limit foods high in cholesterol (eg. shrimp, eggs, whole milk/dairy).
Foods that have been shown to lower cholesterol include soluble fiber (eg. flax seeds, legumes, apples, oat bran) and plant sterols. Monounsaturated and omega-3 fats should also be included in the diet (eg. fatty fish, canola oil, walnuts).
Check out the American Heart Association's main page on cholesterol, which has links to information about healthy lifestyle habits to manage cholesterol levels.
Keep in mind that diet is only one of the factors that can lead to high cholesterol levels. There are other controllable risk factors like, carrying extra weight, having high blood pressure, lacking physical activity, or certain medications.
There are also risk factors that you can't control, such as age and gender, certain medical conditions, and heredity (eg. genetics determining how well your body processes cholesterol can mean you are genetically predisposed to having high cholesterol no matter how well you eat).