Of course the most famous contemporary example of what you're talking about is Frank Abagnale, whose story is told in the book and movie "Catch Me If You Can." He was one of the first people to realize that the increasingly complex American society left gaping holes in which an assumed identity could be exploited, such as posing as a airplane captain and getting free rides all over the world.

But, taking "Con" a little more loosely, you might be interested in Marie Antionnette and The Affair of the Diamond Necklace (which I recently learned about through these lectures), a historical incident that preceded the French Revolution. According to Wikipedia, the con began when "A con artist who called herself Jeanne de Saint-Rémy de Valois, a.k.a. Jeanne de la Motte, conceived a plan to use the necklace to gain wealth and possibly power and royal patronage..."

This question has been removed for running afoul of our "no poll-type questions"; they were banned not for the question, but basically because it was felt these answers didn't produce very good answers. I think this question was one of our very first big, popular Tuesday Trivia threads, however, so you might want to do a search for it!