Another great Bugs Bunny episode is the Wagner one...with Elmer Fudd singing, "Oh, Bwunnhiwde, you'we so wuvewy," and Bugs (all dolled up and on the back of an amazing horse) answering, "Yes, I know it, I can't help it." Etc. It makes me happy just to think about it (even though it does have a suitably operatic tragic end).
Bugs also has the overture to the Barber of Seville: "Welcome to my shop, let me cut your mop, let me snip and chop, Daintily, daintily..."
By the way, I think Bugs is impersonating Leopold Stokowski in the one that was already mentioned. (Everyone excitedly whispers, "Leopold!" as he comes in.)
Wow, I guess we watch a lot of Bugs Bunny around here...it does use a lot of classical music.