This is a great question. I put a bit of thought into this. I think there are several elements involved here - it would need to be a character that is intertwined with a particular universal theme, one whose characteristics are imitated and repeated many times over, and one that has remained relevant since its creation. Using these parameters, I've narrowed it down to two: Hamlet and Sherlock Holmes.
A more recent character that I find most memorable is Odd Thomas from the Dean Koonz books. I never read any of Koonz's books until Odd Thomas. Odd started out as a very ordinary person, who happens to have an extraodinary gift. He is someone I feel for and would like to meet. This is a character I love and want very much to read/learn more about. That and I think he needs a hug :)
Thank you Mary Ellen and Peggy. I am finding the responses here, on Facebook and on Twitter interesting. One person said my question was too vague. That was deliberate. I want to drill down to the core of why we connect, relate and value characters.Thank you for you very well thought out responses.