Just found this thread - so many great songs to choose from Disney.
When You Wish Upon a Star - Pinocchio
Supercalafragilistic, Feed The Birds - Mary Poppins (if this counts)
I Wanna Be Like You, Bare Necessities - Jungle Book
Part of Their World, Under The Sea - The Little Mermaid
Beauty and the Beast, Gaston, Be Our Guest - Beauty and the Beast - I agree a lot of the pieces sound Broadway like, particularly Be Our Guest.
Prince Ali, A Whole New World - Aladdin
You've Got a Friend In Me - Toy Story
When Somebody Loved Me - Toy Story 2:
http://www.youtube.com/watch?v=px0j1EHF8Y0

One of the saddest and most poignant things Disney has done IMO. Randy Newman wrote some great songs.
I Just Can't Wait To Be King, Hakuna Matata, Circle of Life, Can You Feel The Love Tonight - The Lion King
Special mention: Dig a Little Deeper, Almost There - The Princess and The Frog - memorable and catchy toe tappers from Randy Newman, great