Some people make the claim that men are naturally smarter, better at leading, and/or more confident than women. Others, and sometimes the same people, claim that women are naturally more sensitive, compassionate, spiritual, and/or charitable than men. I don't agree with any of those claims. I've known plenty of naturally spiritual and compassionate men, and smart, confident women who are born leaders. I've met women who were jerks and I've met men who couldn't lead anything if their life depended on it. I can't really say that one kind has been more common among men than among women or vice versa.
I believe that the perception that men and women are fundamentally different intellectually or in character derives from the ideas of the society that we have grown up in. We are all imperfect, and those imperfections do not discriminate on the basis of gender. Strengths are also evenly distributed among all of God's children without regard for body anatomy.
This is not to say, however, that I don't think there is any difference at all between the sexes (besides the obvious physical disparities). It's not easy to explain, but I believe that emotionally men and women are different. Not that men don't show emotion and women wear it on their sleeves--that I also think is just part of our culture--but rather that some emotions can be categorized as masculine and some as feminine. Motherhood and fatherhood are prime examples. Although clearly related and mutually necessary, I believe that mothers and fathers have different relationships to their children.
This isn't an easy topic to discuss. The degree to which cultural norms shape our views on the subject is debatable, and it can be a touchy subject to some because of moral or religious beliefs. And perhaps most problematic: every human is either a man or woman, but not both; comparing between the genders is by definition biased, and no one can have first-hand experience about being both male and female. So let's just have a good time discussing and arguing and living through whatever differences there may or may not be between us!
update: there's a very good post at bycommonconsent.com about differences in general, and I really liked a few of the comments that touched on gender differences. Check it out.