|Half-Shot Shooters (1936) [Moe]: Shot to death (along with Larry Fine and Curly Howard) with a cannon by Stanley Blystone on the deck of a ship; we see Stanley pull the lanyard, then the camera pans over to show the Stooges' empty, smoldering boots. (Thanks to Mike)
Three Little Sew and Sews (Three Goofy Gobs) (1939) [Moe a.k.a. Captain Presser]: Killed in an explosion (along with Larry Fine and Curly Howard) when Curly accidentally sets off a bomb while re-enacting their capture of some spies; they are shown as angels sitting on clouds with harps afterwards.
You Nazty Spy! (1940) [Moe Hailstone]: Eaten (off-screen) by lions, along with Larry Fine and Curly Howard, when they try to hide in the lions' den. We see them being chased by the lions, followed by a shot of a lion re-emerging with Moe's hat and belching. (They returned without explanation in the 1941 follow-up I'll Never Heil Again, though only Moe's character had the same name in both shorts.) (This short is available on the compliation The Three Stooges: Stooged & Confoosed.)
I'll Never Heil Again (1941) [Moe Hailstone]: Killed in an explosion (along with Larry Fine and Curly Howard) when Curly detonates an explosive cueball that Mary Ainslee had planted on Moe's pool table. Their heads are shown mounted as trophies on the wall afterwards. (Thanks to George)