Deodato remade Jesu, Joy Of Man’s Desiring into Bachmania. They also released modernized versions of Also Sprach Zarathustra, Prelude to the Afternoon of a Faun, and Rhapsody In Blue, leaving the titles unchanged.
Duke Ellington did a modern version of The Nutcracker march, calling it the Peanut Brittle Brigade. He also did a number called Sugar Rum Cherry based on the Dance of the Sugar Plum Fairies.
Mannheim Steamroller has a modern version of Ride Of The Valkyries.
I’m surprised, saddened really, that no one has mentioned Nigel Tufnell’s piece in D minor, inspired by Bach and Mozart, which admittedly was still a work in progress when he was filmed.
The chorus of Billy Joel’s This Night is the second movement of Beethoven’s Pathétique Sonata. BJ does credit “L.V. Beethoven” as one of the song’s authors.
The second I knew is from Chabrier’s “España”. Googling says the first is based on a passage in Brahms’ Academic Festival Overture, which is based on the student song Was kommt dort von der Höh’, except that the Como song starts on the third of the scale, not the tonic. That’s really stretching the comparison, IMHO. (Additionally, the beginning of the student song sounds a lot like “The Farmer in the Dell”/“A-hunting we will go”. That is credited to Thomas Arne, written in 1777 for “The Beggar’s Opera”.)
Paul Simon’s American Tune is based on a melody line from St. Matthew Passion by J. S. Bach (which itself is based on the song “Mein G’müt ist mir verwirret” by Hans Leo Hassler).
“Cherry Blossom Clinic” by the Movie (from the ***Shazam! ***album) included short snippets of Bach’s “Jesu, Joy of Man’s Desiring” and bits of Tchaikovsky’s “Nutcracker Suite.”
The original lineup of King Crimson used to play Holst’s “Mars, the Bringer of War” in concert. On their second album, they recorded a track called “The Devil’s Triangle” Which was largely based on that Holst piece.
The aforementioned Electric Light Orchestra (Roll Over Beethoven) started their fifth album ‘Face the Music’ with the classic Fire on High. During the first part of the song, the chorus from Handel’s Messiah can be heard in the background.