Lucius Junius Brutus, who feigned madness until the time when he was able to drive the people to insurrection— he more faked stupidity than insanity, causing the Tarquins to underestimate him as a threat.
Alhazen, who was ordered by the sixth Fatimid Caliph, al-Hakim, to regulate the flooding of the Nile; he later perceived the insanity and futility of what he was attempting to do and, fearing for his life, feigned madness to avoid the Caliph's wrath. The Caliph, believing him to be insane, placed him under house arrest rather than execute him for failure. Alhazen remained there until the Caliph's death, thereby escaping punishment for his failure to accomplish a task that had been impossible from the beginning.
King David, in 1 Samuel 21, feigned insanity after being recognized by the servants of Achish king of Gath, a longtime enemy.
Ion Ferguson, an Irish psychiatrist in the British Army in a WWII German prisoner-of-war camp, successfully feigned madness to get himself repatriated. He also assisted two other prisoners in doing the same.