Big in Japan: He was. The Tower Of Death/Game Of Death 2 film was made thanks to a Japanese investor, as well as Japanese demand for more Bruce. This is actually why a good portion of the film is spent in Japan.
Jerkass: There are plenty of anecdotes about his ego, the most well known being the one about the Green Hornet/Batman crossover; Bruce apparently flew off the handle at the revelation that Robin was supposed to beat Kato and threatened to beat the actor to within an inch of his life if the script wasn't changed. The director, mysteriously enough, complied.
Memetic Badass: He beatChuck Norris in Way of the Dragon. As such, he's widely considered among the Internet to have been the most badass man in the world until his death, upon which Chuck took the title.
Papa Wolf: You didn't mess with his kids if you desired mercy.