Curly suffered a stroke during the filming of the short Half-Wits Holiday. He is notably absent from the final scene of the short because he had to be written out of it in order to complete it. His health had been declining for a long time, as evidenced by his frail condition in the shorts leading up to his final one.
Also, the physical comedy was real. Curly had actually gone deaf in one ear from being slapped so much. And Larry had a permanent callous on his left cheek, also from being slapped a lot.
Moe actually broke some of his ribs during the filming of one short in which Curly accidentally saws through the table Moe is standing on, causing it to collapse.
Also from the movie, Curly is played by Will Sasso, who was a cast member on MADtv from 1997 to 2002. On the show, he's known for his impressions of Kenny Rogers (Kenny Rogers' Jackass), Chris Farley (in a COPS parody where the criminals are known celebrities), Bill Clintonnote he also did George W. Bush, but most people remember Christian Duguay and/or Frank Caliendo being better at it, Fred Durst (from Limp Bizkit), and Randy Newman (which was also used on the Family Guy episode "Da Boom"note the Y2K episode)
Not quite as common in the original shorts, although Lucille Ball (back before she was on I Love Lucy) appears in Three Little Pigskins, which was her first credited screen role. They also had once-famed comic Harold Lloyd show up briefly in They Stooge to Conga, and Hoss showed up as 'the Goon' in Outer Space Jitters.
Moe's off-screen persona was a vast contrast to the Jerkass he normally portrayed. While still the "leader" to a fault, he was reportedly very selfless and kind. The Stooges loved to do charity benefits, and stories of them clowning around for sick kids in kids' hospitals are plentiful.
For all that Moe loathed Curly onscreen, when Jerome (Curly) died, Moe mourned his brother deeply.
In addition, perennial supporting player Vernon Dent, who mainly played villains or hot-tempered comic foils, was actually a very generous, friendly, and easy-going person in real life.
Moe, knowing that both Curly and Larry had money troubles (Curly blew his cash on nightclubs and women, while Larry had a gambling problem) convinced them to let him take half their paychecks, which he then invested in their names for their retirement.
Another story about Moe: During the filming of I'll Never Heil Again, the second of the Stooge films to try to put the "wacky" in Those Wacky Nazis, Moe, playing a parody of Hitler, was on set the day of his daughter's birthday when he realized that he was going to be running late if he didn't leave the set immediately. Apparently, the LAPD got a couple of reports of Adolf Hitler running red lights in Hollywood — Howard, wanting to get home on time, didn't even bother to get out of costume!
In his teenage years, Moe was a lifeguard at Brooklyn Beach, and actually has the saving of several lives to his credit.
Old Shame: Although it came later in their careers, they thought it was a mistake to do Snow White and the Three Stooges (since the film gave them little screen time, and barely any slapstick). As well as having scenes involving genuine pathos, which was not in their repertoire.
This actually caused a bit of trouble with The Movie, which was stuck in Development Hell for 11 years because they couldn't find good comic actors to replace the originals. The roles ended up with Chris Diamantopoulos, Sean Hayes and Will Sasso as Moe, Larry and Curly, respectively.
Pie in the Face: Shortly before he died, Moe demonstrated that he still had deadly aim with a pie on The Mike Douglas Show by nailing a mannequin at a range of ten to 15 feet...without his glasses.
The stooges had wanted to do a full-length feature film for years, but weren't able to do one until the late 50s, by which time, Curly was long dead and replaced with Curly Joe.
Curly was supposed to have a part in Malice in the Palace as the cook who the stooges mistakenly think is chopping up a dog and a cat and cooking them, but unfortunately Curly was too sick to play the part so it was given to Larry. Had Curly been able to do it, it would have been the only time Curly would appear in a Shemp short as more than just a brief cameo.