I imagine that in primitive communal societies (such as those of Native Americans), having a single parent had fewer adverse consequences, as there were always adult males and females available to assume the role of surrogate caregiver, but in today's nuclear-family-based societies, it would seem that having two permanent adult caregivers living with the child is very important.
This study concludes that single mothers suffer depression to a higher degree than married mothers:
Bivariate analyses showed that, compared to married mothers, single mothers were more likely to have suffered an episode of depression (12-month prevalence), to report higher levels of chronic stress, more recent life events and a greater number of childhood adversities. Single mothers also reported lower levels of perceived social support, social involvement and frequency of contact with friends and family than married mothers. The results of the multivariate analyses showed that, together, stress and social support account for almost 40% of the relationship between single- parent status and depression. We also found a conditional effect of stress on depression by family structure. Life events were more strongly related to depression in married than in single mothers. -- http://www.ncbi.nlm.nih.gov/pubmed/12910340
And this study (based on a small sample set) suggests that children of depressed single mothers are more likely to suffer behavioral problems:
The findings indicated that mothers who felt increased depressive symptoms were likely to have children with increased behavior problems. Also significant in the data is that mothers in this study who had suicidal thoughts had children who are also likely to have recurring thoughts of death or suicide. These findings highlight the need for increased programs to support families, mothers with depression, and increased access to mental health resources.
-- http://sophia.stkate.edu/cgi/viewcon...ext=msw_papers
I don't think any of this is surprising: It seems obvious that a stable, secure, two-parent family is beneficial to the children. However, many children raised by a single parent have grown up to be happy successful adults.