(Re-posted with links fixed and some other songs added)
People write a lot about how Carl Stalling used the music of Raymond Scott, but one thing you notice if you listen to enough WB cartoon scores is that there's another composer whose work Stalling quoted even more frequently than Scott's: Harry Warren. Warren, with lyricist Al Dubin, wrote most of the songs for Warner Brothers' musicals in the '30s; nearly all the hits from the Busby Berkeley films are by Warren and Dubin. So naturally a lot of their songs found their way into the Warner Brothers cartoons of the early-to-mid '30s, because most of those cartoons were built around WB-owned songs. So for example Tex Avery's 1935 cartoon "Miss Glory" uses the Warren/Dubin song "Page Miss Glory."
When Stalling came to WB in 1936, he later recalled, the thing he liked best about working for a major studio is that he had access to their catalogue of songs. (Whereas when he worked for Disney, he could only use public-domain music, because Disney didn't have the rights to any popular songs apart from the ones his own cartoons introduced.) Over the years he built up a sort of unofficial catalogue of songs that he would quote in specific situations, like quoting Scott's "Powerhouse" for factory scenes. But the composer whose songs he quoted most often was Harry Warren -- and that continued to be true long after Warren had left WB (he went to Fox in the early '40s).
Here are some examples of Warren songs (mostly Warren-Dubin songs, actually) that Stalling used regularly -- but remember that this is only a partial list. Where possible I've linked to examples of how Stalling used the songs.
"The Lady in Red" from In Caliente - Stalling used this song whenever anyone was wearing red, so of course he used it for the opening titles of "Little Red Riding Rabbit."
"At Your Service, Madame" from Stars Over Broadway - Stalling liked to use this one for tea-party scenes. Here it is in a music-only clip from "Rabbit's Feat."
"42nd Street" and "Shuffle off to Buffalo" from 42nd Street, and "Lullaby of Broadway" from Gold Diggers of 1935. Each of these three songs became a standard "New York" theme for Stalling. You can hear each of them in succession in This clip from "Rebel Rabbit".
"Muchacha" from In Caliente - This one turns up in almost every Speedy Gonzales cartoon. Stalling quotes the verse and the refrain of the song in this music-only clip from "Gonzales' Tamales."
And Stalling liked to use the instrumental-only tango from In Caliente, as in "Bully For Bugs."
"Honeymoon Hotel" from Footlight Parade is used for Porky and Petunia's honeymoon in "Porky's Romance."
In a scene from "Slick Hare," patrons dance to Warren's song "Nagasaki" ("Back in Nagasaki where the fellers chew tobaccy and the women wicky wacky woo").
Stalling took up some Warren-Dubin songs from the movie Gold Diggers in Paris as all-purpose "Paris" themes; most frequently he used "The Latin Quarter"; you can hear it at the beginning of "For Scent-Imental Reasons" (and Daffy sings it in the cartoon "Daffy Duck Hunt"), but he also sometimes used "A Stranger in Paree" (it's playing in the Pepe Le Pew cartoon "The Cat's Bah" when Penelope the cat makes her first appearance).
Stalling's all-purpose "sailor" theme was Warren and Dubin's "Song of the Marines" ("Over the Sea, Let's Go, Men"), as you can hear when Tweety sings it in "Snow Business".
For anything dealing with rain and/or the fall, Warren and Dubin's "September in the Rain" was called on ("The leaves of brown came tumbling down, remember?"), as in the beginning of The Hypo-Chondri-Cat".
And of course, "We're in the Money" was Stalling and Milt Franklyn's all-purpose money/wealth theme, as seen here in this brief excerpt from "Baby Buggy Bunny."
And as I said, that's only a partial list. Harry Warren was one of the great songwriters of all time and his WB catalogue, great as it is, is only part of his output (it doesn't include his '40s hits like "Chatanooga Cho-Choo"). But I think it's fair to say that Carl Stalling's scores have had a lot to do with keeping Warren's songs, his WB songs anyway, enduringly popular; people hear "Lullaby of Broadway" and recognize it because they grew up hearing it in cartoons.