Around the clubhouse and practice tee, the answer is as wide as possible....an interstate wouldn't be too wide.
At least 16 behind the practice tee and at least that, if not 24 around the clubhouse. No matter how you try, even painting parking lines, etc. the carts kind of scatter katy wompous and you need more room.
Pete Dye tells the story of being sued at Austin CC for an incident where a woman backed over her sisters leg, breaking it. They got him on the stand, asking whether he had "left enough room for maneuvering carts in the staging area."
He replied (even though he had nothing to do with the cart staging area design) "Well, she backed up without looking, and hit her after moving about two inches. If the cart staging area had been the size of Montana, she still would have hit her!"