I remember long ago when we discovered that the VCR would accept music input from one source and video from another, we put music to our own video.
I remember putting "Learning to Fly" with the skydiving scene from "Point Break" - it fit well timewise too.
A friend put "Live and Let Die" to various mob hit scenes frm "Goodfellas", "The Godfather", and others. Not too bad.
We made a bunch - it was fun. My ultimate would require a budget...
My ultimate scene would be "Gimme Shelter" set to a chase scene where the pursued had no chance of escape, essentially a suicide run. Begins with a bank robbery, most likely. The first two drumbeats and up-tempo would be when the chase starts, maybe as police appear. A view from behind the car as it fishtails down a side street, possibly the rear window shattering from gunfire would occur just as the backup singers go into the first "War, children..."
The woman's cracking voice scream near the end gives me the chills - would be set to a particularly desperate act.
What would your scene be?