|Walter Brennan (1894 - 1974)|
|Kentucky (1938) [Peter Goodwin]: Dies of a heart attack after his horse wins the Kentucky Derby. (Thanks to Rick)
The Westerner (1940) [Judge Roy Bean]: Shot in the stomach during a shoot-out with Gary Cooper in a theatre; he dies after making his way backstage to meet Lilian Bond.
My Darling Clementine (1946) [Old Man Clanton]: Shot in the chest by Ward Bond at the OK Corral, just as Walter is about to shoot Henry Fonda.
The Far Country (1954) [Ben Tatum]: Shot in the back by John McIntire's men in an ambush.
How the West Was Won (1962) [Colonel Jeb Hawkins]: Hit on the head with a chair by James Stewart during a big fight. (Thanks to Brian)
Home for the Holidays (Deadly Desires) (1972) [Benjamin Morgan]: Dies (off-screen) of either natural causes/old age or being poisoned by Eleanor Parker. (Prior to his death, he insists that he's being poisoned, but I don't believe it's ever confirmed whether this was true or just a paranoid belief.) We only see Julie Harris informing his daughters of his death afterwards.