It depends for me.
For parents, they should raise the child as properly as possible for when the child is all grown-up, they would not do anything stupid (in the eyes of society).
On the other hand, each and every individual is responsible for their own specific agendas and actions, and therefore the parents should NOT be responsible for anything the individual does.
An example for those who agree that parents are to blame would be, if I killed somebody regardless of drugs, video games, peers, or any other distractions, why should my parents get in trouble for this? Answer, they shouldn't it is redicious that they could get blamed for something THEY, the parents, have NO, NONE, ZERO, ZIP control over.
Want a better, more historical example? Alright, the Holocaust happened well over 60 years ago, we all have to agree on this. Is it right to make the country of Germany as of the moment of right now, 3:50PM Monday, August 23, 2010 (my time right now) apologize for the events of 60 years ago? When now, that the majority of Germans have NOTHING to do, or never did have any influence on the holocaust. The answer is simply no, because you can't blame somebody or a group for this instance, on something that another individual or group has previously done in the past.
So, for my answer.. No, parents should NOT be blamed for anything not only their child has done, but anyone dead or alive in the world right at this moment, or at anytime in the past (if possible) and the future.