Zero
Master Black Belt
The Gracies have been beat several times. Matt Hughes pulverized Royce Gracie in the first round of their UFC bout in 2006, and Kazushi Sakuraba beat so many Gracies that he became known as the "Gracie Hunter" in Japan. The majority of the people that beat them though learned Bjj first, and then beat them. What added so much to their mystique was the perceived invincibility of Bjj before it was dispersed worldwide, and the bravado at which the Gracies promoted their art.
Love them or hate them, it took balls to put yourself on the line like they did over and over again.
Can't believe no one much remembers or aware of that 2000 Pride match of Sakuraba vs Royce, a marathon 90 minute battle, with Sakuraba coming out on top (that was the one where Coleman (possibly roided to the max (maybe not...)) was unstoppable and took the overall tournament). Sakuraba then later went on to break Royce's arm/elbow when Royce would not submit. One of my favourite fighters, he defeated Royce, Renzo, Ryan and Royler. Those masks were a real hoot also!!!