A fun one which came up recently on IRC: everyone thinks that how your parents raise you is incredibly important, this is so obvious it doesn't need any proof and is universal common sense (how could influencing and teaching a person from scratch to 18 years old not have deep and profound effects on them?), and you can find extended discussions of the best way to raise kids from Plato's Republic to Rousseau's Emile to Spock.

Except twin studies consistently estimate that the influence of 'shared environment' (the home) is small or near-zero for many traits compared to genetics and randomness/nonshared-environment.

If you want to predict whether someone will be a smoker or smart, it doesn't matter whether they're raised by smokers or not (to borrow an example from The Nurture Assumption*); it just matters whether their biological parents were smokers and whether they get unlucky.

This is so deeply counterintuitive and unexpected that even people who are generally familiar with the relevant topics like IQ or twin studies typically don't know about this or disbelieve it.

(Another example is probably folk physics: Newtonian motion is true, experimentally confirmed, mathematically logical, and completely unintuitive and took millennia to be developed after the start of mechanics.)

* Rich's citation is to Rowe 1994, The Limits of Family Influence: Genes, Experience, and Behavior; from pg204:

But this interpretation foolishly neglects to consider the genetic component of parent-child similarity. Table 7.2 summarizes reports of two twin studies, an adoptive study, and a family study. In all these studies, the offspring of smokers were adults at the time they were surveyed. Smoking's heritability averaged 43%, whereas smoking's rearing environmental variation was close to zero. [Shared rearing variation (c^2): N/A (family, Eysenck (1980)); <0% (Twin, Cannelli, Swan, Robinette, & Fabsilz (1990)); <0% (Twin, Swan, Carmelli, Rosenman, Fabsitz, & Christian (1990)); <0% (Adoptive, Eysenck (1980)); mean: 0%] In other words, effects of rearing variation (e.g. parents' lighting up or not, or having cigarettes in the home or not) were nil by the time the children had reached adulthood. In Eysenck's (1980) report on adoptees, the smoking correlation of biologically unrelated parent-child pairs was essentially zero (r = -.02). Parental smoking may influence a childs risk through genetic inheritance: The role of parents is a passive one-providing a set of genes at loci relevant to smoking risk, but not SOCially influencing their offspring.