Can a board of directors remove one of its own? In the case of a California corporation, the answer is no. The power to remove directors is vested in the shareholders and the superior court pursuant to Corporations Code Section 303 and 304. While technically not a removal, one option may be available to a board. Section 302 provides that the board may declare vacant the office of a director who has been declared of unsound mind by an order of court or convicted of a felony.
I guessing that while some directors may believe that their fellow members are non compos mentis or even criminals, they usually aren't able to back their opinions with judicial declarations. In any event, I was unable to find any reported decisions in which Section 302 was actually invoked. This suggests that there aren't many insane or felonious directors.