Seeing as how Mount Rushmore dedicates the most influential presidents, I'd say that influence on the medium matters more than popularity of quality in this area. That said, I'd probably say...
Atom/Astro Boy - The most famous of Osamu Tezuka's characters. Got to have a character from the man known as "The God of Manga".
Yabuki Joe - Ashita no Joe helped elevate the sports genre with it's psychological introspection and capturing of the Japanese youth at the time, remaining the best sports manga of all time, and remained a heavy influence to any boxing series to come after it. The fact there's a bench dedicated to it's most famous scene which is also referenced in nearly every referential anime is testament to it's legacy.
Char Aznable - Whilst series such as Tetsujin 28 founded the Super Robot genre and Mazinger Z refined the idea, Mobile Suit Gundam is what truly elevated the Mecha genre's potential in both style and substance, so adding it's most popular and best character seems appropriate for what's now the most financially successful anime/manga in terms of merchandise. I could have picked Shinji from Evangelion for the series taking even bolder steps for the genre, though the series acted more of a critique of the genre than fully revolutionising it when considering very few emulated it's formula (plus the Rebuild movies ended up regressing it's evolution of the genre).
Son Goku - Whilst Kinnikuman and Kenshiro did far more in laying the foundations of the Shonen demographic, Son Goku not only inspired far more modern Shonen protagonists, but Dragon Ball was one of the key factors in anime gaining an international appeal.