^ Agreed.
Answering your question - I think they affect us greatly. Take my father for example. He was an alcoholic. He smoked cigarettes every day. He died young (53.) Now I don't have a father. My family has to pay for his mistakes. My mother is close to losing their house, I'm working 60 hrs./week, seeing a psyciatrist, a councelor, and taking medication to deal with depression...
However, you can take a similar situation and have a different viewpoint.
My friend's mother died when he was 12. His father is an alcoholic, a drug addict, a serial law breaker. My friend, however, leads a somewhat normal life - albeit he is a drug addict, and his motto is Life's a B***** and then you die so F*** the world, let's all get high. He claims the same that you do...that his father's mistakes don't affect him. 'I am the master of my own destiny.'
I believe the past determines your present, but you determine your future. You may have a strong moral character because your parents weren't there - at all - and you had to learn how to be strong and depend only on yourself...but one could argue that that is a reaction - a by-product of the reality that is you were abandoned and now you are a co-dependant work-a-holic.
It's all in how you look at life. 90% of the battle happens between your ears.