Our friends at About.com have this to say:

The first documented instance of a public figure 'flipping the bird' was in 1886, pop culture historians say, when famed ball player Charles 'Old Hoss' Radbourn covertly extended his middle finger while posing for a team photo with the Boston Beaneaters. It's been a downhill slide for American manners ever since, according to an article by George Basler in the Binghampton Press & Sun-Bulletin. Social critics complain that the increasing prevalence of casual bird-flipping in public — arguably a trend of cosmic proportions these days — signals a disturbing vulgarization of the culture. As to the oft-disputed origins of the once-taboo gesture, experts insist the digitus impudicus goes all the way back to ancient Greece, not the 1415 Battle of Agincourt, as alleged in a popular email factoid.