I've titled this thread as great music in the movies rather than from the movies because sometimes the music was around first!
And to kick things off, a real "classic" in every sense of the word - the iconic opening to Rollerball with Toccata & Fugue in D minor by Johann Sebastian Bach.
The piece was originally written for organ, and the rendition used in the movie was easily the best available at the time (in my opinion anyway). I've heard others which were technically brilliant, but didn't quite manage to pull off the dramatic impact of this one.
But like any truly great piece of music, it has been reinterpreted more than a few times.
A great example which sticks to classical instruments would be the incredibly talented Vanessa-Mae with the Berlin Philharmonic Orchestra:
Classical instruments - yes, but with a very modern twist.
Finally, here's an example of a modern, electronic genre interpretation, the Electronica rendition by Galbatron:
All works of art in their own way, based on a classic that was brought back to fame in modern times by the futuristic movie Rollerball.