I always thought Duck Amuck was the greatest cartoon ever made. And it has Bugs in it, albeit in a minor (yet pivotal role).
But if I had to go with one that is a true Bugs cartoon it would be hard to beat “What’s Opera Doc?”
Hmmm My favorite has the lines (Abridged version)
“All right Rabbit all right where is he”
“He’s not in the stove…”
“Oh Ho So he’s hiding in the stove eh?”
“Would I turn on the gas if he was hiding in the stove?”
“You might rabbit you might…” ETC
That’s Bugs & Thugs. The link is for the IMDB page, since I can’t access YouTube at work.
Yes that is the one!!!
Ah, so many good Bugs toons. But I agree with a previous poster that my favorite is the Hunter’s Trilogy of “Rabbit Fire”, “Rabbit Seasoning”, “Duck!Rabbit!Duck!”. I can watch them over and over. I also especially like the ones where one of the characters “played artist” and wreaked havoc on another character, such as in “Duck Amuck” and “Rabbit Rampage”. In fact, I have to go watch them now!
Asking someone to choose their favorite Bugs Bunny cartoon is like asking them for their favorite child or their favorite body part. It cannot be done!
But of those not mentioned yet, I always loved “Baseball Bugs” and the one where Binky Buzzard says, “I was a little too smart for him.” The way he says that gets me every time!
I love all the cartoons mentioned, but my favorite Bugs is “Hare To Heir” (or vice versa), with Yosemite Sam playing the English baron on the verge of bankruptcy, when Bugs arrives to offer him a million pounds if he can restrain his temper. Mel Blanc’s fake swearing for Sam in this picture never fails to put me on the floor.
Stop that music, ya crazy rackin’ frackin’ varmint rabbit!!!
I don’t know if saw it more than once, but an older one that had Bugs and Elmer dealing with an outbreak of “wabbitosis” was hilarious, as I recall.
I also like the one with the vampire:
“Abaca-pocus”
“Hocus-cadabra”
“Newport News”
“Walla-walla Washington!”
I still catch myself humming, “La-da, dee-dee, da-da, dee-dee, da-da, dee-dee, da-da, da-abacadaaaaaaa-bra”.
Transylvania 6-5000, again an IMDB link because I can’t open YouTube at work.
And the rabbitosis one is Hare Tonic.
Interesting comments over at Metafilter.
Jones agrees with me!!! SCORE!!! 
I can’t believe no one has yet mentioned my favorite, Long Haired Hare. Bugs conducting a pompous opera singer, cumulating with Bugs having the singer hold a note so long that the guy’s collar bursts and he turns six shades of purple. Home of the famous line, “Of course you realize, this means war!”
I’d say he agrees with ME more!
(Because, while you posted that opinion before me, I got more specific for my reasons, which are the SAME reasons Jones expressed! So there! 
Of course, I don’t blame you for not realizing this, seeing as how my post is being roundly ignored by everyone… sniff)
Unfortunately, I never saw “What’s Opera Doc” until I was out of college.
One of the reasons this is so sad relates to a specific tradition at Caltech.
Each day of finals week, nearly all the stereos in the dorm are hooked together to play “The Ride of the Valkyries” at full volume at 7 am. Because of the stress which is thereby associated with this music, playing it at any other time is punishable (on the first offense) by being forcibly hauled off to the showers, clothes and all. (Subsequent offenses may result in being dumped into a particularly algae infested pond.) When one of the alumni was an astronaut, it was arranged to wake him up by playing “The Ride” over the radio. Medical telemetry showed a tremendous increase in his heart rate!
If I’d seen WUD back then, I would have arranged to have the Elmer Fudd rendition substituted at least a couple of times a year.
Ooh, thanks for reminding me! This gives me an excuse to post one of the funniest articles ever written: An analysis of Bugs Bunny’s baseball career
Beaky Buzzard, actually. Also known as “the Snerd Bird” after his Mortimer Snerd voice.
Is that the one who hums “I’m Bringin’ Home A Baby Bumblebee”?
There’s so many of them, but one of my top ones is Hillbilly Hare. The way he takes over the square dance and makes the bumpkins maul each other is hilarious.
“That thar rabbit varmint’s gots to be around here someplace. On account of I sees his footy-prints!”
I also really like the one with Bugs and Babyface Finster. One of the few times the villain actually gets the better of Bugs (at first, anyway).
You are correct! And the cartoon I was referring to was “Bugs Bunny Gets the Boid” 1942.
For me, it’s a close race between What’s Opera, doc? and Rabbit of Seville, but I have to give it to What’s Opera, Doc?.
I’ll KILL the wabbitt !!!
This is one of my favorites, as well!
“Twirl, twirl, twist an’ twirl. Jump all around like a flyin’ squirrel…”