Wikipedia concurs:

Etymology
While the exact origins of the phrase are unknown, it is commonly believed to have been invented by Americans during World War II. Large numbers of American troops were stationed overseas for many months or years, and as time passed many of their wives or girlfriends decided to begin a relationship with a new man rather than wait for their old one to return. As letters to servicemen from wives or girlfriends back home would typically contain affectionate language, a serviceman receiving a note beginning with a curt "Dear John" (as opposed to the expected "Dear Johnny", "My dearest John" or simply "Darling" for example) would instantly be aware of the letter's purpose.

There are a number of theories on why the name John is used rather than any other. For starters, John was a common name in America at the time. John is also the name used in many other terms that refer to an anonymous man or men, such as "John Doe" or "John Q. Public". Further, there existed prior to World War II a radio programme starring Irene Rich which was presented as a letter written by a gossipy female character to her never-identified romantic interest. It was both titled and opened with the words "Dear John", and may have contributed to the genesis of the term.

Retrieved from "http://en.wiktionary.org/wiki/Dear_John_letter"

And here's another take:

"The expression seems from the evidence to have been invented by Americans during the Second World War. At this time, thousands of US servicemen were stationed overseas for long periods; many of them found that absence didn't make the heart grow fonder. The unhappy news was necessarily communicated in a letter. A writer in the Democrat and Chronicle of Rochester, NY, summed it up in August 1945:

"Dear John," the letter began. "I have found someone else whom I think the world of. I think the only way out is for us to get a divorce," it said. They usually began like that, those letters that told of infidelity on the part of the wives of servicemen... The men called them "Dear Johns".
Why Dear John? That isn't entirely clear but a couple of pointers give a plausible basis for it. John was a common generic name for a man at this period (think also of terms like John Doe for an unknown party to a legal action). Such letters were necessarily written in a formal way, since any note of affection would obviously have been out of place. So a serviceman getting a letter from his wife or girlfriend that started so stiffly knew at once that a certain kind of bad news had arrived.

Several subscribers have mentioned a song on the theme of receiving a "Dear John" letter, suggesting it was the origin of the phrase. However, online sources say it appeared only in 1953, several years after the phrase had become established. A more plausible source was suggested by Dick Kovar — in a pre-World War Two radio programme called Dear John, starring Irene Rich, which was presented as a letter by a gossipy female character to her never-identified romantic interest and which opened with these words. Proving a link is likely to be impossible, but it's conceivable this played a part in the genesis of the term.

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A