Some more facts about Bugs Bunny:
Bugs’ name came from his animator. In 1938, Ben “Bugs” Hardaway was redesigning a new rabbit character. A fellow employee casually referred to the drawing as “Bug’s Bunny” (which was written above the illustration) and the name stuck ever since.
Bugs Bunny’s carrot-chewing stance came from ‘It Happened One Night. There is a scene with Clark Gable leaning against a fence and eating carrots while talking with his mouth full.
The story that Mel Blanc was allergic to carrots dates back at least to 1945, when animators told the New York Times that Mel Blanc would chew a carrot and spit it out, otherwise he’d get sick. But both his autobiography—That's Not All, Folks!—and Chuck McKibben, operations manager at Mel Blanc Studios, give a different story: McKibben told The Straight Dope that Blanc wasn’t allergic to carrots—he just chewed one and spat it out so that he could keep recording his lines (although McKibben does point out that Mel didn’t like “anything healthy”).
Bugs Bunny is a U.S. Marine. At the end of the 1943 short Super-Rabbit, Bugs wears a USMC blue uniform. As a result, they made Bugs an honorary private of the corps. Throughout WWII, Bugs continued to be promoted in rank until he retired as a Master Sergeant.
In 1961, Blanc got in a serious car accident that left him in a coma for weeks. Eventually, a doctor tried to get the unresponsive patient to talk by asking him, “Bugs Bunny, how are you doing today?” Blanc responded in Bugs’ voice, “What’s up, Doc?” Later, the doctor would say of the incident,“It seemed like Bugs Bunny was trying to save his life.”
And last but not least: The sight of Bugs Bunny chewing a carrot is among the best–known images in cartoon history, but root vegetables are in fact bad for rabbits. Carrots have a lot of sugar in them and can cause tooth decay for rabbits if they eat too many of them.