Rocky was first created in 1946 because many of Bugs Bunny's past foes (such as Beaky Buzzard, Elmer Fudd and Yosemite Sam) were considered very stupid, and that Friz Freleng needed a more intelligent (and challenging) figure to face the rabbit.
Rocky and Mugsy are a pair of gangsters that appear in the shorts. Rocky, the leader and brains of the two, is the short one with the black hair, a hat that covers his eyes, and is constantly seen smoking a cigarette, and Mugsy, Rocky's henchman, is a big stupid oaf.
Rocky first appeared in the 1946 film Racketeer Rabbit where Bugs decides to find himself a new home, but the one he chooses is unfortunately occupied by a duo of bank robbers. The characters here are called "Rocky" (drawn like movie gangster Edward G. Robinson) and "Hugo" (a caricatured Peter Lorre).
Freleng liked the Mobster idea, and so Rocky later appeared in Golden Yeggs as a criminal who wanted Daffy Duck because he thought he could apparently lay golden eggs which were actually done by a goose although Mugsy didn't appear with him; he had a number of different henchmen with the main one named Nick and he made a deal with Daffy that if he couldn't lay a single golden egg he would kill him and when the time comes he shoots Daffy in the head causing him to actually lay a golden egg, but the catch was he had to lay enough to fill an egg carton. Beginning from this cartoon, Freleng redesigned Rocky, making him a more generalized caricature of the "tough guy" gangster rather than Edward G. Robinson in particular. Freleng used several of the same techniques that would make Sam, his other Bugs villain, such a humorous character: Despite Rocky's tough-guy demeanor, everlasting cigar (or cigarette) and foppish gangster clothing, he really is little more than a dwarf in a much-too-large hat.
Rocky and Nick reappeared in Catty Cornered where they kidnapped Tweety because he was worth a lot of money, but Sylvester unknowingly rescued him after attempting to eat him many times and he was greatly rewarded.
Rocky next appeared this time with Mugsy in his first appearance in Bugs and Thugs where they unknowingly kidnapped Bugs Bunny after robbing a bank they concluded that he knew too much and held him hostage. Bugs attempted to call for help at a gas station but they saw through him and yanked him away from the phone, later on he tricks them into getting hit by a train which they survive afterwards, they force him to rebuilt their car and drag the car to their hideout. Once there Rocky orders Mugsy to kill Bugs by saying "You know what to do, let him have it!" while entering the room he points his gun at Bugs and Bugs says "You heard him let me have it" and he stupidly gives him the gun and he shoots Mugsy in the face and he stumbles next to Rocky and says "Duh, I let him have it boss, just like you said", then he faints and lands on top of Rocky, who punches him off. Next Bugs makes a siren sound and pretends to be a cop by using a thick Irish accent and he tells them to hide in a stove, then he goes into a conversation with himself pretending to be a cop, he says "Where's Rocky? Where's he hiding?", "He's not in the stove!", "Ho-ho, he's hiding in the stove, eh?", "Look pal, if my friend Rocky was in there, would I toin on the gas and toss a lit match inside?", "You might rabbit, you might", "I guess he's not here, let's go Clancy", immediately afterwards a real cop shows up (with exactly the same voice that Bugs uses) and they go through exactly the same routine but this time when he turns on the gas they run out and beg themselves to be arrested.
They appeared next in Bugsy and Mugsy in which Bugs makes Mugsy do things that cause him to get hit by Rocky and their fighting eventually leads to them getting arrested, Mugsy looked completely different from the previous short and depicted as being thinner and having a big chin.
They last appeared in The Unmentionables in which Bugs Bunny is an undercover detective come to arrest them; he does so by trapping them in cereal boxes, in this appearance Mugsy looked like he did in Bugs and Thugs.
They make a very small cameo in The Looney Tunes Show. They appear in a book of people that the police have arrested before. There are other older characters in there like Hugo.