The earliest character I can think of is Odysseus, the protagonist in Homer's Iliad. Before Homer, of course, there are the Greek playwrights, but I don't know their characters nearly as well. I think the Iliad and the Odyssey have the greatest public recognition, particularly since Hollywood has taken an interest in them over the years.
Last year, Sela Carsen wrote a great article about mythology, in which she talks about the ancient gods and goddesses as sources of ideas for stories. Before classical literature, stories were told of these beings and their trials and tribulations as they mirrored, and reflected back to humanity, peoples' behavior.
I think that's the point of telling stories, in many ways. We tell stories about ourselves, to ourselves, in an effort to better understand the world around us and the people with whom we must get along. People are confusing and stories help us make our way through the pitfalls that inevitably arise whenever more than one person gathers together or tries to accomplish something.