The tragic hero infamous for his downfall due to hubris in Greek myths is Oedipus. His excessive pride and determination to defy prophecy led him to unknowingly kill his father and marry his mother, Jocasta. This catastrophic realization brings about his ruin, as he gouges out his eyes in despair. Oedipus's story serves as a cautionary tale about the dangers of arrogance and the inevitability of fate, themes that resonate deeply within Greek tragedies.