There are many different conditions that involve the heart, and some are more likely to run in families than others. Inherited heart diseases are those that run in families and are caused by a mutation (or change) in one gene (or in a number of genes). There are many categories of inherited heart disease, including cardiomyopathies, arrhythmias, aneurysms/dissections, and familial hypercholesterolemia. See here for more information about each of these.
Most of the inherited heart diseases are passed down in an autosomal dominant pattern and often show up in multiple generations in a family.
Many other heart diseases can run in families in different inheritance patterns. Some of these are caused by genetic factors only; however, they often are caused by combinations of genes that are passed down and environmental factors, including diet, exercise, smoking, ethnicity, gender and more. If you have a family history of high cholesterol, heart attacks or stroke, you may have an increased risk for these types of heart disease. Working to change factors such as your diet and exercise habits can help reduce your risk.