Eventually at most only 21 million coins for 6.8 billion people in the world if it really gets big.
But don’t worry, if Bitcoin ever gets really big, the currency unit can always be divided further. Each coin can be subdivided into 100,000,000 units. The display of sub-cent amounts can be added later if they’re needed.
I anticipated that some day there would need to be very small fractions of a bitcoin. The internal representation of amounts is already in the smallest unit. The display of amounts is a separate issue and can be changed later.