The Boys Club of America teaches young men leadership skills, camping and social skills.

From Twitter:

Which is correct?
Boys Club
Boy’s Club
Boy Club
Boys’ Club

Answer And Explanation
Well, they are all correct except number 2, but they all mean different things:
First, number 2 is incorrect without an article, as in A Boy’s Club;

Boys Club means a place you can go to find boys
Boy’s Club means one boy’s club, owned by him.
Boy Club either means a club for boys or a club of boys or both.
Boys’ Club means a place of , for and owned by boys

I have no purpose except to teach you style (which includes punctuation). There is no inappropriate reference here. I thought of this, because all around Tokyo one sees ‘Girl’s Bar,’ which is incorrect. It means one girl owns a bar, and it is incorrectly written. I didn’t use the example of a “girly bar” (the correct usage), because I think these places are sad, exploit women, fleece lonely and incapable men and ruin relationships; tragically, they offer jobs to young women who deserve to be offered government education and training programs. I did not want to call attention to girly bars. Also, in America, the Boy Scouts is sometimes referred to as a “boys club.”

Photo: Kyle Glenn