On one of my writing loops, someone asked how much of a role to give her bit players. Now this was in reference to an epic fantasy novel, which often has a "cast of thousands." As for short stories, a lot of the advice we hear amounts to "less is more." With this in mind, peopling our stories effectively is perhaps one of the most difficult things we do. One of my longer short stories has a cast of about fifteen identified characters, with others milling about. I thought about cutting it back, but the protag is a soldier in an army. He has only his own head for privacy. The story needs to feel crowded.
At the opposite end of the spectrum, I've read stories with one character: the protagonist. This is rarely enough because the most interesting antagonist is an actual character. But whether you prefer a minimalist approach or a more populated cast, one thing is clear. Every character must serve to forward the plot, setting, and characterization. The test: if a character is removed, can the story still progress? If so, kill that darling.