The example that I'm sure many will remember is the parade scene from Ferris Bueller's Day Off, which features both Wayne Newton's recording of "Danke Schoen" and the Beatles' covering the Isley Brothers' "Twist and Shout". The scene stands out as a great example of using popular music to develop a character: Ferris' larger-than-life performance situates him as the guy that everyone wants to be. We understand the kind of bombastic person that he is.
Another example comes from Pretty in Pink, where Jon Cryer's character enters a record shop and dances to Otis Redding's "Try a Little Tenderness", in order to impress Molly Ringwald's character.
The most iconic use of music in Hughes' filmography comes at the end of The Breakfast Club, which features Simple Minds' "Don't You (Forget About Me)". It's possible that no song and film are as tied together as these two.