I don’t know its name, but there’s a song based on the beginning of the 3rd movement of Rachmaninoff’s Symphony #2, before the clarinet solo.
Stretching the world “pop” but No Other Love as recorded by Jo Stafford is based on Chopin’s Etude in E major, Op. 10.
It’s a very lovely melody which also turns up in this Argentine tango.
Ooh that reminds me that Beethoven’s Fifth Symphony was the basis for “A Fifth of Beethoven,” by Walter Murphy and the Big Apple Band. … which was heavily sampled by Robin Thicke in “When I Get You Alone.”
Elvis (or his songwriters, anyway) did this a couple of times. There’s also “Can’t Help Falling in Love,” which is based on the French art song “Plaisir d’Amour,” and “Today, Tomorrow and Forever” based on Liszt’s gorgeous piano piece, Liebestraum.
Going back to the fifties, “Stranger in Paradise” was a big hit for Tony Bennett, from the musical Kismet – and was based on Alexander Borodin’s Polovetsian Dances from Prince Igor. (All of Kismet was based on Borodin’s music.)
Back in the 50s, Peter Sellers borrowed Clarke’s “Trumpet Voluntary” for the newish medium of rock and roll, creating “Trumpet Volunteer”. It may be a novelty song, but it’s quite catchy.
Rob Dougan (electronic) uses Chopin’s Prelude in E minor (op 28 no 4) as the foundation for Clubbed to Death 2.
Bliss N Eso (Australian hip hop) use Tchaikovsky’s Swan Lake ballet suite as a basis for Destiny Lane.
So many of the melodies of well-known popular songs were actually written by the great masters. Like these familiar themes.
Emerson, Lake and Palmer also used an instrumental chunk of Lieutenant Kije (“Troika”) for their song “I Believe in Father Christmas”.
This is what I came in here to say. At least he gave credit where credit is due… in the liner notes for the album, it says “verse by Billy Joel, chorus by L.v. Beethoven”. 
Oh oh, we forgot a very obvious one:
Never Gonna Fall In Love Again -Eric Carmen
Jesus, did he write any songs that weren’t based on Rachmaninoff?
Jackie Wilson’s “Night” from the 1960s. Taken NOTE FOR NOTE from an Aria by Camille Saint Saens’ “Samson and Delilah.” One of the few classical robberies I don’t mind. I actually like it almost as much as the original.
http://www.youtube.com/watch?v=9piRiiZ0C4Q (Skip to 1:25 for the comparison)
ALMOST. 
Franz Lehar’s up for grabs in…10 years or so? I don’t remember how long copyright law is good for, he died in '48. I’d listen to a Taylor Swift cover of his Vilja aria from the Merry Widow!
I was thinking of this thread earlier when I remembered Pitbull’s “Hey Baby” quotes Grieg’s “In the Hall of the Mountain King.” He tends to quote or sample other people’s compositions in his songs. Though this isn’t classical, I just wanted to mention it - he used a sample in his song “Bon Bon” from Yolanda Be Cool & D Cup’s “We No Speak Americano,” which itself sampled Renato Carosone’s “Tu Vuo’ Fa’ L’Americano.”
Oh, and the Beatles’ “Because” is supposed to be “Moonlight Sonata” played backwards–though I’ve listened to it in reverse, and I don’t hear it, myself.
Blue Oyster Cult throw in a quick snippet of that in “Joan Crawford” as well.
(Of course, Apocalyptica just play the whole damn thingbut that’s another thread entirely.)
No way, the tunes are completely different.