Peggy Lee as Peg the dog in Lady and the Tramp. Peg has just the one song, He's a Tramp. But what a song! As Lee co-wrote all the songs and also voiced the Siamese Cats and Darling (Lady's owner) - and they get songs too despite little screen time - it's like several Wonders for the price of one.
Another example from Disney is the snake Kaa from The Jungle Book who tries to hypnotize Mowgli and fails. He is only in the film for two scenes (he was actually going to be in just one in development, but his popularity with some test audiences gained him another one), The voice is by Sterling Holloway, of all people. He did the voice of Winnie the Pooh, which is part of the reason why he's so funny.
Also, King Louie, who has just one scene (and musical number), but is very fondly remembered as a highlight of the movie.
Also from the same movie, Shere Khan, who despite being the Big Bad, is only onscreen for about 10 minutes and doesn't appear till about 3 quarters of the way in, but he's remembered as fondly as other Disney villains that have more screen time than he does.
The Backson in Winnie the Pooh (the 2011 movie) literally has one scene lasting under a minute, but it's a very memorable one.
Princess Aurora herself in Sleeping Beauty. She remains silent for most of the movie, with very few dialogue whatsoever, and the only time she ever opened her mouth completely is when she sang "I Wonder" and "Once Upon A Dream", respectively.
Mrs. Jumbo from Dumbo. Like her son, she actually remains silent throughout the entire film, only saying Dumbo's real name after he's been delivered to her by a stork.
In Chicken Little one of the most popular characters is Morkubine Porcupine he only has five minutes of screen time and he only says three words.