My newly-discovered 4th cousin once removed Jon alerted me to the fact that New Hampshire marriage and divorce records are now online at Ancestry.com. The divorce records only go up to 1938-- for obvious reasons, privacy would be an issue for records more recent than this.
Jon found a divorce record for his 2nd great-grandparents; his 2nd great-grandmother divorced his 2nd great-grandfather, who had been a veteran of the Civil War and and an Andersonville POW, for drunkeness (can't really blame him for drinking, considering the hell he no doubt went through-- no VA or couselling back then!). I also found a divorce record for my great-aunt from her first husband.
Going through the divorce records, I was rather surprised that there were so many. Divorce was supposed to be a rare thing in the 19th and early 20th centuries, but there were literally thousands of records for New Hampshire.
I noticed that the person initiating the divorce was almost always the wife, and that the most common reason given was abandonment. The second most common reason that I came across was "extreme cruelty." The only other reasons I saw were for drunkeness and adultery.