We have already seen, in an earlier post on the chapter on parenting in Freakonomics, how parenting has been shown to have a small effect on the development of a child -- in particular, intellectual development, as measured by the child's academic performance in school. Personally, I find this position quite liberating: it's good to know that my screw-ups as a parent has only a small effect on our child ;-)
The origin of this liberating insight can be traced to the book The Nurture Assumption by Judith Rich Harris (do check out this site; it has tons of information that you will find useful). Apparently (and I haven't read her book, so I may be a little imprecise here), in her recounting of research, parents' influence is about 50%, and it is largely through their genes; and, the remaining 50% is influenced by the child's peers far more strongly than by the parents.
Two caveats. First, intellectual development is just one aspect of a child's personality, so it is possible that other aspects (moral? religious?) where parenting styles and tactics might play a role. Second, while parents' influence is smaller than that of peers, the former still get to decide who the child's peers are (through their choice of where they live, which school the child attends, etc).
Laura, over at 11D and Harry Brighouse, at Crooked Timber, are discussing what appears to be a fascinating book: Unequal Childhoods: Class, Race and Family Life by Annette Lareau (you can read the first chapter on the book's website). I won't summarize the discussion here, except to say that it will give you some new ways of thinking about parenting.