Animated: "Cats Don't Dance". It's one of the best animated films, in my opinion, but it's sadly not very popular. Why, I don't know. The music, characters and story are all brilliant and the movie in general has a lot of heart.
Live-action: That's a toughie, but I'll have to say "It Happened One Night". It's from 1934, so it's definitely not new, but that is what makes it a classic - along with the great acting and adventurous, romantic story.