Say what you will about The Movie, but there's a moment they got out of the way early on. The three start out as orphans, and Moe is the first to get adopted, his new parents declaring that day as his birthday and asking him what he would like. Moe's big wish - for his two friends to join him. They return to the orphanage only to ditch him there.
Needless to say, Curly and Larry are very taken aback when they discover the truth years later.
In Real Life Moe made Larry and Curly give him part of their paychecks each time. He then put it in a savings account for them, doing so because he knew of Larry's gambling addiction and Curly spending his money on ladies and booze. Because of this all of them were able to retire, and Curly was able to get the medical care he needed after his stroke.
Shemp, having had enough of Ted Healy, decided to leave the Stooges and pursue a solo career. Though he was hesitant about it, Moe encouraged him to go for it. Not only did Shemp have a successful solo career, but his departure allowed Curly to join the Three Stooges.
After Curly's stroke that forced him to retire, Shemp willingly gave up his solo career and returned to the Stooges, because he knew Moe and Larry would be unemployed if he didn't.
The culmination of this was the short "Hold That Lion!," in which the retired Curly made a cameo appearance. That was the only time all three of the Howard/Horwitz brothers appeared in a Stooges short.
The Stooges when at their most heroic. In "Nutty but Nice", they try to reunite an Ill Girl with her kidnapped father; it's one of the few shorts to have an unambiguously happy ending.
"Disorder in the Court," while having the typical Stooge antics, centers around them doing their best to help prove a fellow entertainer innocent of murder.