My parents were both heavy drinkers and my father used drugs fairly often. Does this mean I am susceptible to becoming addicted to drugs or alcohol because they were?
It has been demonstrated that alcoholism and drug addiction are genetically inherited diseases. Yes, just with high blood pressure, obesity and diabetes, if you have a positive family history, meaning, someone in your biological family has had the illness, you are at increased risk for developing the illness yourself. The good new is, you know that you are at increased risk for alcoholism and other types of drug addiction, so you can make decisions that will prevent you from developing the illness. The safest way to make sure you don't become addicted is to not drink or use drugs at all. If that is not a realistic option for you, then you certainly want to be sure that you don't use alcohol or drugs when you are in a period of stress, as your risk of becoming addicted will be increased during those times. Finally, know the early warning signs of addiction (drinking or using more than you intended, others are annoyed by your use, using first thing in the morning etc.) and if you start to see those signs in yourself, seek help immediately.
The book Is Alcoholism Hereditary?: One in Six Families in America Is Affected by Alcoholism. Here Is the Answer to Their Most Pressing Question is a great resource that can answer your question even more in depth. It is an oldie but goodie, and will give you a good understanding of the genetics of alcoholism.