It sounds like a joke, and that's the way it started in 1932. But almost every day since then, the ducks have paraded through the lobby of the elegant old Peabody Hotel, marching to music on a red carpet to the delight of international visitors. Every morning at 11:00 they march from the elevator to the fountain, and after a day of splashing around, they march back to the elevator at 5:00, where they are taken to their rooftop 'penthouse'. You can follow them up there and learn more about them from the hotel's official duck master.
If you go:
This has become an extremely popular attraction, so you should stake out your viewing spot early.
Links:

149 Union Street
Memphis, Tennessee 38103 USA
Phone Numbers:
Peabody Hotel
+1 (901) 529-4000
+1 (901) 529-4000