Just to add to what Turnbull said regarding Brando's calming influence: Lenny Montana, who plays Luca Brasi, had no prior experience in acting, and his first scene to film was that of when Luca thanks the Done on the day of his daughter's wedding. With the camera facing Lenny and looking over Brando's shoulder, when Lenny was about to deliver his lines, Brando stuck his tongue out, attached to which was a piece of paper with the words "F**k You" (not CERTAIN on that specific detail though) written on it, sending Montana into fits of laughter.

Another time was when they were filming the return of the Don from hospital. The two guys carrying The Don's bed upstairs struggled mightily. It was because (they would later learn) Brando had weighed the bed down with loads of weights. ;D

Mick