He stole from the second movement of Rachmaninov's Piano Concerto #2 for "All by Myself." He stole from the third movement of Rachmaninov's Symphony #2 for "Never Fall in Love Again."
In doing so, he continued in the honored tradition of Neil Diamond and Alan & Marilyn Bergman, who stole from the second movement of Rachmaninov's Symphony #2 for "You Don't Bring Me Flowers." And who could forget 1945's "Full Moon and Empty Arms," stolen from the third movement of Rachmaninov's Piano Concerto #2 by Buddy Kaye and Ted Mossman?
Sergei Rachmaninov would have been thrilled to know that his music lived on in the popular form. (He loved jazz!) He would have joyfully hummed those melodies as he deposited his royalty checks in the Beverly Hills branch of United California Bank.
Sting's Russians borrows from Prokofiev's Lieutenant Kijé Suite
A 60's song Nut Rocker is based on Tchaikovsky.
Carmen thought Rachmaninov's 2nd Concerto was public domain. It wasn't, it was still under copyright, so after the song was released, he got a thick envelope from the Rachmaninov family's lawyer informing him that he could choose between paying them royalties or defending a lawsuit for copyright infringement.
Happily, his lawyer got together with the Rachmaninov family's lawyer, and they worked out a royalty deal that allowed him to also use the slow movement from the 2nd Symphony for "Never Fall in Love Again".