This hopping Easter creature is believed to originate from Germany. The first known account of der Osterhase is found in the 1684 notes of a Heidelberg professor of medicine, where he discusses the ill-effects of overeating Easter eggs. German and Dutch settlers later brought the notion of der Osterhase or Oschter Haws (dutch) to the U.S. in the 1700's.
As in other parts of the world, German, Swiss and Austrian children will hunt for their Easter eggs and goodies on Easter Sunday morning all over their home and yard. Sometimes children make and leave a nest out the night before for the Easter bunny to leave treats in.
Currently a new Osterhasenmuseum is being planned in Oberwesel am Rhein, Germany. See their museum website for all sorts of Easter bunny photos and more info.