It's not common for it to be legal except in very specific situations. I don't know if it's American, but they do it here a lot in dense cities for deliveries. It's not a true parking, like for hours, it's for running in and out.
It's called "stopping" and not "parking" when you stop (and potentially even turn off your engine and leave the vehicle unattended) to make a delivery or load/unload.
In many places it's considered parking, legally, anytime you stop and place the car in park.