That varies by location quite a bit. I can generally walk in my local pharmacy and have a prescription filled in a few minutes. Maybe more like 15 minutes if it's a controlled substance. But as a practical matter I just walk in, pay, and pick it up, my doctor sends the prescription over electronically. And lately, any recurring prescriptions are handled by mail anyway.

Have I ever experienced that "come back in an hour" phenomenon? You bet. Then I went to a different pharmacy.