Okay, we've looked at both Bugs Bunny and Daffy Duck individually, and now it's time to focus on some of the best cartoons in which the two cartoon heavyweights shared the screen (much to Daffy's consternation, I'm sure). Bugs Bunny didn't necessarily meet his match with Daffy, but the two characters played off one another in a manner that seemed more substantive than Bugs' usual battles with the likes of Elmer Fudd and Yosemite Sam. While someone like Elmer would simple come at Bugs with guns blazing, Daffy would often try to match Bugs on an intellectual level, and usually wind up having his bill shot clean off his face. These are my favorite Bugs and Daffy cartoons:
Bugs Bunny and Daffy Duck
Rabbit Seasoning (1952): An ever-malleable Elmer Fudd finds himself repeatedly shooting Daffy, despite Daffy trying to convince him it isn't duck season. Actually, it is duck season, but Bugs uses reverse psychology and clever pronoun usage to trick Daffy into somehow begging Elmer to shoot him. There's also an important lesson for all of us in this cartoon, which is that a crazy man with a gun can always be thwarted by a rabbit dressed as a woman.
Beanstalk Bunny (1955): Daffy Duck plays "Jack" in this cartoon. He's duped into trading for magic beans which grow into a giant beanstalk, and in no time at all he and Bugs find themselves at the mercy of a giant Elmer Fudd. The relationship between these two characters is illustrated quite well in the scene where their trapped under a glass dome. Their voices blocked by the glass, all we see is Daffy going insane while Bugs merely stands their, calm and collected (he had a glass cutter the whole time). Eventually, Daffy's greed for the giant's gold gets the better of him, and he ends up playing Elmer's wristwatch.
Bugs Bunny and Daffy Duck
Duck! Rabbit, Duck! (1953): Essentially a continuation of "Rabbit Seasoning," this short once again finds Bugs and Daffy trying to convince Elmer to shoot the other. Admittedly, the idea couldn't have been stretched too much further, but it's still a great short, and I loved the end when Bugs tells Elmer it's neither rabbit nor duck season, but baseball season. I also love Elmer's line when Bugs dons an angel costume to trick Elmer into thinking he killed him: "Sorry mister rabbit, I hope I didn't hurt you too much when I killed you."
Show Biz Bugs (1957): Whenever I see something on television or on the movie screen where it feels like someone is trying too hard to make a point, or to be liked, I always compare them to Daffy Duck in this cartoon. Upset that he has second billing to Bugs Bunny, he eventually turns their stage show into a competition which sees Bugs Bunny showered with applause while Daffy receives little more than quiet indifference. He does finally get his adulation in the end, but only by drinking a lot of dangerous chemicals and blowing himself up.
Bugs Bunny and Daffy Duck
Daffy, probably the first and last duck to travel underground with Bugs Bunny, finds himself in Ali Baba's cave, surrounded by treasure. Seriously, what is it about Albuquerque that always causes Bugs Bunny to become disoriented? Anyway, Daffy's greed gets the better of him, and while Bugs manages to escape the clutches of the cave's guard, Daffy ends up shrunk by a curse.
Bugs Bunny and Daffy Duck
Bugs Bunny and Daffy Duck
Baby Bugs Bunny
Baby Bugs Bunny
Baby Bugs Bunny 
Bugs Bunny Lola Bunny
