To the best of my knowledge, John Wayne only died in:
The Shootist - He is killed in a gunfight in at the end of the film.
The Cowboys - He is killed by Bruce Dern's character.
The Alamo - Playing Davy Crockett, he is killed by a Mexican soldier's lance.
Sands of Iwo Jima - He is killed by a sniper's bullet at the end of the film.
Wake of the Red Witch - He dies as the ship sinks.
The Fighting Seabees - He is shot by a sniper.
Reap the Wild Wind - He is killed by a giant squid.