Freakonomics looked at this, coming up with some interesting conclusions. For one thing, reading to your children didn't seem to have any effect on education scores, but owning books did (did the babies inherit book-reading genes?). Another example: adopted children tended to conform to the lifestyle predicted by their biological parents, not their adoptive parents, in regards to crime and income (which implies some uncomfortable ideas about poverty and class). I don't remember the exact details of their analysis, but the general approach was to take commonly accepted statistical measurements and check for correlations. The most specious claim in the book (AFAIK) was that legalized abortion leads to lowered crime-rate twenty years down the road; while this is probably true, I don't think the evidence demonstrates anything beyond correlation. His chapter on babies, though, was pretty good.

I've only met one pair of twins who were distinctively divergent (though both were in the military), but I believe they were fraternal.