According to his biography, he was "born" in 1940 in Brooklyn, New York and the product of many fathers: Ben "Bugs" Hardaway (who created a prototypical version of the character in 1938), Bob Clampett, Tex Avery (who developed Bugs' definitive personality in 1940), Robert McKimson (created the definitive Bugs Bunny character design), Chuck Jones, and Friz Freleng. According to Mel Blanc, his voice actor, his accent is an equal blend of someone from the Bronx and someone from Brooklyn.
He is noted for his catchphrase of "Eh, what's up, doc?" and his feuds with Elmer Fudd, Yosemite Sam, Marvin Martian, Daffy Duck, and even Wile E. Coyote, who usually takes on the Road Runner. Almost invariably, Bugs comes out the winner in these conflicts, because that is in his nature. This is especially obvious in films directed by Chuck Jones, who liked to pit "winners" against "losers". Worrying that audiences would lose sympathy for an aggressor who always won, Jones found the perfect way to make Bugs sympathetic in the films by having the antagonist repeatedly bully, cheat or threaten Bugs in some way. Thus offended, (usually three times) Bugs would often drawl "Of course you know, dis means war" (a line which Jones noted was taken from Groucho Marx) and the audience gives Bugs silent permission to inflict his havoc, having earned his right to retaliate and/or defend himself. Other directors like Friz Freleng had Bugs go out of his way to help others in trouble, again creating an acceptable circumstance for his mischief. When Bugs meets other characters who are also "winners", however, like Cecil the Turtle in Tortoise Beats Hare, or, in World War II, the Gremlin of Falling Hare, his record is rather dismal; his overconfidence tends to work against him.
Bugs Bunny has some similarties to figures from mythology and folklore, and might be seen as sort of modern trickster.
"Bugs" or "Bugsy" as a nickname means "crazy".
History
A suggested early influence
A number of animation historians believe Bugs to have been influenced by an earlier Disney character called Max Hare. Max, designed by Charlie Thorsen, first appeared in the Silly Symphony The Tortoise and the Hare, directed by Wilfred Jackson. The story was based on a fable by Aesop and cast Max against Toby Tortoise, and won the Academy Award for Animated Short Film for 1934. Max also appeared in the sequel Toby Tortoise Returns and the Mickey Mouse cartoon Mickey's Polo Team.
The only solid connection between Max and Bugs however is Charlie Thorsen. He was also responsible for the redesign of Bugs from a white to a gray rabbit for his third appearance Hare-um Scare-um (see below), thus the similarity in design.
Proto-typical rabbits
Bugs Bunny first appeared in the cartoon short Porky's Hare Hunt, released on April 30, 1938. The short was co-directed by Cal Dalton and Ben Hardaway whose nickname was "Bugs". The cartoon had an almost identical theme to a 1937 cartoon, Porky's Duck Hunt, directed by Tex Avery and introducing Daffy Duck. Following the general plot of this earlier film, the short cast Porky Pig as a hunter against an equally nutty prey, who was more interested in driving his hunter insane than running away. But instead of a black duck, his current prey was a tiny, white rabbit. The rabbit introduces himself with the expression "Jiggers, fellers," and Mel Blanc gave the rabbit a voice and laugh that he would later use to voice Woody Woodpecker. In this cartoon, he also quoted Groucho Marx for the first time (from the movie Duck Soup): "Of course, you know, this means war!"
His second appearance was in 1939's Prest-O Change-O, directed by Chuck Jones, where he serves as the pet rabbit of Sham-Fu the Magician, an unseen character. When two dogs enter the house of his absent master while seeking refuge from a storm, the rabbit starts harassing them, but is ultimately bested by the bigger of the two dogs.
His third appearance was in another 1939 cartoon, Hare-um Scare-um, directed by Dalton and Hardaway. Gil Turner, the animator for this short, was the first to give a name to the character. He had written "Bugs' Bunny" on his model sheet, meaning he considered the character to be Hardaway's. This short was also the first where Bugs was depicted as a gray bunny instead of a white one; the redesign having been done by Charlie Thorsen (see above). The short is notable as featuring Bugs' first singing role and also the first time where he dresses in drag to seduce his antagonist. Following this short he was given the name "Bugs" by the Termite Terrace animators in honor of his creator, Ben "Bugs" Hardaway. "Bugs" or "Bugsy" as a name also fit the Bunny's early characterization, as it was popular vernacular for "crazy".
His fourth appearance was in the 1940 short Elmer's Candid Camera by Chuck Jones. There, both Bugs and Elmer Fudd were redesigned to the appearances that would become familiar to audiences. It was also the first meeting of the two characters.
Bugs emerges
Bugs' true personality would then emerge in Tex Avery's A Wild Hare, released on July 27, 1940. It was in this cartoon that he first emerged from his rabbit hole to ask Elmer Fudd, now a hunter, “What's up, Doc?" It is considered the first fully developed appearance of the character. Animation historian Joe Adamson counts A Wild Hare as the first Bugs Bunny short, with the previous shorts being different one-shot bunnies bearing only coincidental resemblance to Bugs.
Bugs then made a cameo in Robert Clampett's Patient Porky, first released on September 14, 1940 to announce the birth of 260 rabbits. His seventh appearance finally introduced the audience to the name Bugs Bunny, which up till then was only used among the Termite Terrace employees. It was Chuck Jones' Elmer's Pet Rabbit, released in January 1941. It was also the first short where he got top billing. He would soon become the most prominent of the Looney Tunes characters as his calm, flippant insouciance endeared him to American audiences during and after World War II.
Read more at Wikipedia.org