This might be difficult to understand but I’ll try my best to describe what I’m looking for:
Original, written-specifically-for-the-movie songs from movies that AREN’T traditional song-and-dance musicals (a la Singin’ In the Rain) that are in some way integral to the plot. Sung by the cast (or at least lip-synced) is a good indicator.
NOT just songs off the soundtrack
NOT songs from “music videos” within the movie (“Danger Zone”)
NOT songs just playing in the background
NOT songs that existed long prior to the movie (“La Bamba”)
There are probably going to be a lot of songs from mockumentaries and movies about fictional bands.
Examples:
“That Thing You Do”
“Let’s Duet” (Walk Hard)
“On the Dark Side” (Eddie and the Cruisers)
“Somebody Kill Me” (The Wedding Singer)
Almost anything from This Is Spinal Tap
“Rock and Roll High School,” from the movie of the same name featuring the Ramones. The plot (such as it is) revolves around P.J. Soles’ character having written that song for them, and trying to get them to listen to it and record it themselves.
I’m Tired from Blazing Saddles Always Look On the Bright Side of Life from Life of Brian Springtime For Hitler from The Producers
also Aimee Mann’s Wise Up from Magolia although she actually wrote it for Jerry Maguire and although it’s on the soundtrack it wasn’t in the movie.
Maybe not completely “original”, but “Home in the Meadow” (Greensleeves) in “How the West Was Won”.
This song is as integral as it gets as it is passed down (and sung) by various members of the different generations of the pioneering family.
***Postcards from the Edge *** was not a musical, but it ends with newly sober Meryl Streep trying to reinvent herself as a country singer and performing Shel Silverstein’s “I’m Checking Out.”
“Feel My Heat,” as performed by Dirk Diggler and Reed Rothchild in Boogie Nights. Diggler also performed “The Touch,” but that was a cover of the seminal Stan Bush song.
“Jai Ho” from Slumdog Millionaire, because you just can’t have a Bollywood movie without at least one big dance number with the whole cast. And there’s no other good way to wrap it up.
“Wise Up” by Aimee Mann in the movie Magnolia might or might not count. It wasn’t written specifically for the movie, but it hadn’t been used before. And it could be seen as a music video in the movie, but that scene is a part of the plot.