The only reason this show went off the air was because star David Carradine quit the series. He had sustained so many injuries, he felt he could not go on. The show got high ratings all three seasons it aired.
According to Bruce Lee's widow, Linda Lee Cadwell, Lee originated the concept and was intended to star in the series, but David Carradine was cast because the network felt the American audience was not ready for an Asian actor as the lead and Lee received no credit for his concept. (This was dramatized in Dragon: The Bruce Lee Story (1993).) But according to the producers, although Lee was consulted and was considered for the role, they created the concept and Carradine was always their first choice.
In several episodes, a younger Kwai Chang Caine was played by Keith Carradine, David Carradine's younger brother. Their other brother Robert Carradine and their father John Carradine also appeared in episodes (as Sonny Jim and Serenity Johnson, respectively).
David Carradine had no formal martial arts training of any sort. He had received some training as a dancer when he was younger. This was a particularly aggravating fact for Bruce Lee after he was turned down for the part of Caine.