Indeed, a lot of data suggests that a countries level of income equality and citizens happiness is negatively correlated.
http://en.wikipedia.org/wiki/Economic_inequality#Effects_of_...
http://en.wikipedia.org/wiki/Economic_inequality#Effects_of_...
Unfortunately, women tend to be attracted to relatively rich men, which can result in a lower "supply" for relatively poor men if a rich man can attract several women (for instance, by using serial monogamy). It's been suggested that this leads to a larger amount of violence in poor neighborhoods (due to increased competition among men).
Which leads to another problem: Being relatively poor may not be a problem, provided the level of wealth is secure. Due to the lack and inefficiency of social safety nets in the US, however, being relatively poor can always turn into being poorer still.
Since being relatively poor often means living in a relatively poor neighborhood with a higher prevalence of violence, there's a good reason for feeling insecure all the time. Your son may get killed in a drive-by shooting, while your daughter may get raped. Meanwhile, you may get robbed.
Even if one's situation is not as critical, it's always possible to become critical. For instance, one may simply loose one's job, and thus the means to provide for a family. Or one becomes ill. The number one reason for declaring personal bankruptcy in the US are medical bills. A large percentage of these people were health insured, by the way.
These are just a few examples on the top of my head.