According to
Kendler et al (2005), women usually report having more supportive social networks than men, but have higher rates of depression. In a study of over 1,000 pairs of male-female twins, Kendler et al found that women reported having a more supportive social network than did their twin brothers. Male and female twins did not show a significant difference in the amount of support received from their parents. Kendler et al found that social support was a better predictor of depression in women than in men.
Shih et al (2006) suggest that these differences begin with greater reactivity and exposure to social episodic stress as adolescent girls.
Brugha et al (2005) found that small social networks (< 3) were especially detrimental to men.
Piccinelli and Wilkinson's 2000 review points out that studies on social support and depression are inconsistent, with some showing advantages for women and some for men.
I feel incredibly lucky to have the social support that I do. I spent most of my life very socially isolated, first by being in a rural community as part of an unpopular family, and later by being in a romantic relationship where outside friendships were discouraged. While women are supposed to be more affiliative than men, in my life, the most supportive friendships I've seen have been between men, in my father and his friends.