Shana, I definitely think people are profoundly influenced by their parents' values -- principally by modelling -- and it may be that in many cases this influence will ultimately win out. But I also see many parents -- and parents-to-be -- overestimating this influence. "Oh, I would never let my kid do/think/say X", or "What did I do wrong that my kid is doing Y?" I think it is grounding for parents to realize that they are only one voice in a sea of influence. Maybe the most important voice in the long run, but their kids are not simply creatures for them to mold and shape. Kids see the world, and make their own decisions.
(This is also borne out, in my experience in, for instance, language acquisition. Kids often by six or seven speak the language of their playmates as or more fluently than that of their parents.)
I think this is much more obvious if you are trying to teach values that diverge sharply from the values of the society around you. If your kids' parents' playmates, their teachers, etc., all share more or less similar values to yours, it is easy to convince yourself that your influence is larger than it is, because you are discounting the reinforcing effect of the larger environment.
One should also not underestimate the influence of siblings -- I think Aviva may be as great an influence on Noah as I am!
JB, thank you... I like to post on parenting, when I can get my text through the censors (Aviva and Noah vigilantly inspect all mentions of themselves).