Kathryn R. Johnson and Claudia Persico a new NBER working paper exactly on this subject:
Between 2000 and 2008, access to high-speed Internet increased significantly in the United States, but there is debate over whether access to high-speed Internet improves or harms well-being. We find that a ten percent increase in the proportion of county residents with access to high-speed Internet leads to a 1.01 percent reduction in the number of suicides in a county, as well as improved health self-reported mental and physical. We further find that this reduction in suicide deaths is likely due to economic improvements in counties with access to high-speed internet. Counties with increased access to high-speed internet see decreases in poverty rates and unemployment rates. Additionally, zip codes that have access to high-speed internet are seeing an increase in employees and establishments. Furthermore, the heterogeneity analysis indicates that the positive effects are concentrated in the working age population, that is, between 25 and 64 years old. This trend is precisely what studies linking economic conditions to suicide risk predict.
It appears that broadband is indeed (was?) good for you.