Well, beyond obvious anatomical differences and artificial discrepancies generally associated with one's upbringing, I suppose the most notably innate psychological discrepancies I can think of are sexual behavior and general (albeit obviously not universal) personality traits that tend to correspond consistently to one sex or another, especially in more egalitarian societies. For instance, women consistently exhibit a higher degree of jealousy than men in relationships, and women consistently tend to exhibit personable traits more often than men.
But, generally speaking, it's admittedly fairly difficult to accurately gauge the extent to which differences between the sexes are innate or culturally acquired. It's essentially an argument over nature versus nurture, and the extent to which the various aspects of differences between the sexes actually exist innately has been a fairly contentious issue for quite some time. Overall, I believe it's rational to conclude that there's no strong evidence of many significant, innate social and psychological differences between the sexes relative to the extent to which both genders share similar traits, and that human cognition and social adaptability arguably plays a greater role in exaggerating differences between them -- or creating differences, for that matter.
Overall, I do acknowledge that differences between both genders exist, and that a handful of these are both significant and arguably innate, but I'm not convinced that most of these differences are mostly the result of innate psychology.