Someone has finally made the connection that has been obvious for a while: states that allow gay marriage have significantly less divorce than those that don't. "States That Allow Same-Sex Marriage Have Lower Divorce Rates," by Edward McClelland at NBC 5 Chicago, lists each state's divorce rate (it doesn't say for what year), grouped into those that allow gay marriage and those that don't.
It has long been observed that the "red" states have much more divorce, along with most other kinds of social problems and disruptions, than the blue states. Specifically, divorce has always been lowest in the northeast and the upper midwest. Those states are more Catholic, Lutheran and Jewish, religions that correlate with more stable families. People there have somewhat more liberal beliefs but more traditional lives than in the South and West.
Northerners are more "socially rooted". When I moved to Rhode Island for college, unlike many students I got to know the locals pretty well and even studied them for some of my classes. Ordinary people there were closely supervised by relatives, priests, and other figures in their community -- very different from the often socially isolated, transient, military and private-sector famliies in the high-growth suburban stretch of the "sunbelt" where I grew up. The kind of people who'd leave a marriage, I realized, were the kind of people who would already have left Rhode Island. And vice-versa. Southerners, on the other hand, are simultaneously the most traditionalist and the most individualistic, hedonistic, wild and impulsive Americans, as Florence King pointed out in one of her greatest works, Southern Ladies and Gentlemen.
It has likewise been observed that states with Major League Baseball teams (historically more prevalent in Northern states) have less divorce. Other factors that are probably actually causal, not merely correlated: Northerners have more education and wait until they are older to marry, both of which are strongly related to stronger marriages and less divorce. The Northeastern and Upper Midwest states include the states the longest divorce waiting period laws in the US, although they also include some with little or no waiting period. It has also been suggested that those with more modern, egalitarian attitudes and habits do better at marriage.
As for actual divorce rates for gay couples, and some other interesting facts about gay marriages, see this insightful 2011 article by Frederick Hertz about U.S. gay marriages, and a 2004 study finding higher divorce in Swedish gay marriages than straight ones.