Bugs Bunny was first introduced in 1940 in his definitive form.
The year needs a small historical qualification. An unnamed rabbit prototype appeared in Porky’s Hare Hunt in 1938, and related versions appeared in several later cartoons. However, A Wild Hare, released on July 27, 1940, is widely regarded as Bugs Bunny’s first official appearance.
That Tex Avery short established the familiar character: a confident gray rabbit, voiced by Mel Blanc with his recognizable New York-influenced delivery, casually outsmarting Elmer Fudd. It also introduced Bugs’s famous “What’s up, Doc?” catchphrase.
The name itself appeared on-screen later, in Chuck Jones’s Elmer’s Pet Rabbit in 1941. This is why some timelines list 1938 for Bugs’s prototype, while standard trivia questions asking when Bugs Bunny was introduced generally expect 1940—the year of the fully developed character.