From Wikipedia, a list of popular songs from the past century that incorporate classical compositions.
(1891) "O Promise Me" by Reginald DeKoven & Smith, from the musical Robin Hood -- based on Musica proibita, the name popularly given to an aria in the 1888 Italian opera Mala Pasqua by Stanislo Gastaldon.
(1913) "Hungarian Rag" by Julius Lenzberg - based on the Second Hungarian Rhapsody by Franz Liszt.
(1918) "I'm Always Chasing Rainbows" by Joseph McCarthy and Harry Carroll - based on the Fantasie Impromptu in C Sharp Minor by Frédéric Chopin.
(1919) "The Marine Hymn" by L. Z. Philips - based on an air from Jacques Offenbach's Genevieve de Brabant
(1919) "Peter Gink" by George L. Cobb - based on the Peer Gynt Suite by Edvard Grieg.
(1922) "Goin' Home" popularized by Paul Robeson - based on the "Largo" from Dvorak's Symphony No. 9, "From the New World"
(1928) "Lover, come back to me" in The New Moon by Sigmund Romberg - the middle section is based on "June: Barcarolle" from Tchaikovsky's The Seasons, opus 37b.
(1930) "In an Eighteenth-Century Drawing Room" by Raymond Scott - based on Mozart's Piano Sonata, K. 545
(1937) "Song of India", arr. Tommy Dorsey - based on a theme from Rimsky-Korsakov's Scheherazade
(1938) "My Reverie" by Larry Clinton - based on Debussy's Rêverie
(1939) "The Lamp is Low" - Peter DeRose and Bert Shefter - based on Maurice Ravel's Pavane pour une infante défunte
(1941) "Tonight We Love", by Freddy Martin, Bobby Worth and Ray Austin - based on Tchaikovsky's Piano Concerto in B-Flat Minor
(1945) "Full Moon and Empty Arms", by Buddy Kaye and Ted Mossman - based on Sergei Rachmaninoff's Piano Concerto No. 2.
(1946) "Summer Moon" by Klenner, sung by Lauritz Melchior - based on Igor Stravinsky's The Firebird (Ronde des princesses)
(1952) "The Bigger The Figure", by Louis Prima - based on Rossini's Largo al factotum from The Barber of Seville.
(1953) "Stranger in Paradise" by George Forrest and Robert Wright, in the Broadway musical Kismet - based on a theme from Alexander Borodin's Polovetsian Dances
(1956) "Hot Diggity (Dog Ziggity Boom)" by Al Hoffman and Dick Manning - based on a theme from Chabrier España, Rhapsody for Orchestra
(1958) "Catch a Falling Star" by Lee Pockriss and Paul Vance - based on a theme from Brahms' Academic Festival Overture
(1959) "Once Upon a Dream" in the Disney movie Sleeping Beauty - based upon a waltz in Tchaikovsky's ballet Sleeping Beauty.
(1960) "Asia Minor" by James Wisner - based on Edvard Grieg's Piano Concerto in A minor.
(1960) "It's Now or Never" by Elvis Presley - based on 'O Sole Mio by Eduardo di Capua.
(1961) "I Can't Help Falling In Love With You" by Elvis Presley - based on Plaisir d'Amour by Jean Paul Egide Martini.
(1962) "Nut Rocker" by B. Bumble and the Stingers - based on Tchaikovsky's "March of the Wooden Soldiers" from The Nutcracker .
(1963) "Hello Mudduh, Hello Fadduh! (A Letter From Camp)" by Allan Sherman - based on Ponchielli's "Dance of the Hours" from La Gioconda.
(1964) "Rap City" by The Ventures - based on Johannes Brahms' Hungarian Dance No. 5 in G minor.
(1965) "A Lover's Concerto" by The Toys - based on J.S. Bach's Minuet in G from the Anna Magdalena Notebook.
(1966) "Past, Present and Future" by The Shangri-Las - based on Ludwig van Beethoven's Piano sonata No. 14, "Moonlight"
(1966) "A Groovy Kind of Love" by The Mindbenders - based on the Rondo section of Muzio Clementi's "Sonatina in G major," op. 36 no. 5.
(1967) "Imitation Situation" by Fever Tree (San Francisco Girls) - used opening passage of J.S. Bach's Toccata_and_Fugue_in_D_Minor
(1967) "A Whiter Shade Of Pale" by Procol Harum - (loosely) based on J.S. Bach's Orchestral Suite No. 3, Air (commonly known as Air on a G String) and Cantata 140 "Sleepers Awake".
(1967) "Ding! Dong! The Witch is Dead" by The Fifth Estate - based partly on Michael Praetorius's "Dance Suite Terpsichore"
(1968) "Emerald City" by The Seekers - based on Beethoven's Ode to Joy from his Ninth Symphony.
(1968) "Hall of the Mountain King" by The Who - inspired by Edvard Grieg's "Peer Gynt Suite".
(1968) "Prelude B - I'm so Glad" by Deep Purple on Shades of Deep Purple - nicely lifted from Rimsky-Korsakov's Scheherazade: "The Sea and Sinbad's Ship".
(1968) "Variations on a Theme by Erik Satie" by Blood Sweat & Tears - based on "Trois Gymnopédies" by Eric Satie
(1968) "Rain and Tears" by Aphrodite's Child - based on Pachelbel's Canon in D Major
(1968) "Daydream" by the Wallace Collection (band) - based on Pyotr Ilyich Tchaikovsky's Swanlake
(1968) "All You Need is Love" by The Beatles contains a snippet from the beginning of J.S. Bach's "2-part Invention no. 8".
(1969) "Albinoni's Adigio in G Minor" by The Doors on Boxed Set Disk 1 Without a Safety Net - based on Tomaso Albinoni's Adagio
(1969) "Because" by The Beatles - inspired by Ludwig van Beethoven's Piano sonata No. 14, "Moonlight"
(1969) "Jane B" by Serge Gainsbourg for Jane Birkin - based on Frédéric Chopin's "Prelude No. 4"
(1969) "Mars: The Bringer of War" by King Crimson on Epitaph - a progressive rock arrangement of Mars, from the The Planets suite by Gustav Holst
(1969) "Sabre Dance" by Love Sculpture - based on Aram Khatchaturian's "Gayane"
(1969) "Bourree" by Jethro Tull, arrangement of bourree from J.S. Bach's suite in E minor for lute/guitar.
(1970) "The Devil's Triangle" by King Crimson - middle section based on Mars, from the The Planets suite by Gustav Holst
(1970) "The Barbarian" by Emerson, Lake and Palmer - Allegro barbaro, for piano by Bela Bartok
(1970) "Knife Edge" by Emerson, Lake and Palmer - based on Sinfonietta, first movement by Leos Janacek. 2nd part of lead break is lifted from the Allemande from French Suite No. 1 in D minor by Johann Sebastian Bach. (Said piano piece is quoted note for note up to the repeat sign in the middle.)
(1970) "A Song of Joy" by Waldo De Los Rios for Miguel Rios - based on Beethoven's Ninth Symphony
(1971) "Baby Alone In Babylone" by Serge Gainsbourg for Jane Birkin - based on the 3rd movement of Brahms's Symphony No. 3
(1971) "The Only Way" from Tarkus by Emerson, Lake and Palmer - intro and lead break are quoted from two different compositions by Johann Sebastian Bach, namely Toccata in F major for organ (up to the end of the F pedal point) and Prelude in D minor from Book I of the Well-Tempered Clavier.
(1972) "American Tune" by Paul Simon - based on the hymn "O Sacred Head" by Johann Sebastian Bach
(1972) "Abaddon's Bolero" by Emerson, Lake and Palmer - possibly inspired by Boléro by Maurice Ravel, but very different theme, meter (4/4 instead of 3/4), and atmosphere
(1972) "Also Sprach Zarathustra" [I] by Deodato - a funk arrangement of Richard Strauss' composition of the same name
(1972) "Cans and Brahms" by Yes - based on Johannes Brahms Symphony No. 4, third movement
(1972) "Hoedown" by Emerson, Lake and Palmer - based on Rodeo by Aaron Copland
(1972) "Horizons" by Steve Hackett from Genesis on Foxtrot - (loosely) based on 1st movement of 'Suite For Cello in G major, by J.S. Bach
(1972) "Joy" by Apollo 100 - based on Jesu, joy of man's desiring by J.S. Bach
(1972) Pictures at an Exhibition by Emerson, Lake and Palmer - entire album based on the work by Modest Mussorgsky, with two original pieces ("The Sage" and "The Curse of Baba Yaga")
(1972) "Song Sung Blue" by Neil Diamond - based on Mozart's "Piano Concerto No. 21", second movement
(1973) "Joybringer" by Manfred Mann's Earth Band - based on "Jupiter - bringer of jollity" from Gustav Holst's The Planets suite
(1973) "Toccata" by Emerson, Lake and Palmer - based on Ginastera's First piano concerto, fourth movement
(1974) "Annie's Song" by John Denver - based on Tchaikovsky Symphony No. 5, second movement
(1974) "Minuetto Allegretto" by The Wombles - based on Mozart's "Symphony No. 41"
(1974) "Voices of Syn" by Klaus Schulze on Timewind - incorporates a collage of Verdi songs sung by an operatic singer.
(1974) "Danse Macabre" by Esperanto, (a multinational Progressive Rock band) - their own version of the Danse Macabre by Camille Saint-Saëns.
(1975) "Song of Scheherazade" by Renaissance - inspired by Rimsky-Korsakov's Scheherazade
(1975) "Could It Be Magic" by Barry Manilow - quotes extensively from Chopin's Prelude in C minor
(1975) "Fanfare for the Common Man" by Emerson, Lake and Palmer - based on Aaron Copland's work of the same name.
(1975) "I Believe in Father Christmas" by Emerson, Lake and Palmer - based on Lieutenant Kije Suite, Opus 60, by Sergei Prokofiev (released as a single under the name of Greg Lake alone).
(1976) "All By Myself" by Eric Carmen - based on Sergei Rachmaninoff's Piano Concerto No. 2
(1976) "A Fifth of Beethoven" [I] by Walter Murphy - disco version of Beethoven's Fifth Symphony, featured in Saturday Night Fever
(1976) "Ma Lou Marilou" by Serge Gainsbourg - based on the 1st movement of Beethoven's Piano Sonata No. 23 in F minor "Appassionata" (opus 57)
(1976) "Never Gonna Fall In Love Again" by Eric Carmen - based on Rachmaninoff's Second Symphony
(1977) "If I Had Words" by Scott Fitzgerald and Yvonne Keeley - based on Camille Saint-Saëns' Symphony No. 3 ("Organ Symphony")
(1977) "Rockaria" by The Electric Light Orchestra - based on "Un Bel Di" from Puccini's "Madame Butterfly"
(1978) "Lady Lynda" by The Beach Boys - based on J.S. Bach's Jesu, Joy of Man's Desiring
(1979) "If I Had You" by The Korgis - based on Rachmaninov's "Variations on a theme by Paganini" Variation 18, based on Paganini's "Caprice No 24 in A minor"
(1980) "Swan Lake" by Madness - based on Tchaikovsky's "Swan Lake"
(1980) "Toccata" by Sky - based on Bach's Toccata and Fugue in D Minor
(1981) "Can Can" by Bad Manners - a manic ska version of the Can-Can from Jacques Offenbach's "Orpheus in the Underworld"
(1981) "Difficult to Cure" by Rainbow - based on Beethoven's "Ode to Joy" (last movement of the ninth symphony).
(1983) "This Night" by Billy Joel - adapted from Beethoven's Pathétique Sonata
(1984) "Coming Bach" by Alcatrazz - based on Johann Sebastian Bach's "Bourrée" from Lute Suite No. 1, BWV 996.
(1984) "Icarus Dream Suite" by Yngwie J. Malmsteen - based on Tomaso Albinoni's Adagio.
(1984) "Madame Butterfly" by Malcolm McLaren and the World Famous Supreme Team - based on Giacomo Puccini's opera Madame Butterfly.
(1984) "Rite of Spring" by Birdsongs of the Mesozoic - based on Igor Stravinsky's work of the same name
(1985) "Lemon Incest" by Serge Gainsbourg for Charlotte Gainsbourg - based on Frédéric Chopin's "Étude No. 3 in E (Tristesse)" (in opus 10)
(1986) "Russians" by Sting - based on "Romance" theme from Lieutenant Kije Suite, Opus 60, by Sergei Prokofiev
(1987) "Lost Song" by Serge Gainsbourg for Jane Birkin - melody after part of Edvard Grieg's "Solveig's song" (in Peer Gynt, Suite No. 2, opus 55)
(1989) "And So It Goes" by Billy Joel is based on the hymn Jerusalem by Charles Hubert Parry.
(1989) "Black Star (live)" by Yngwie J. Malmsteen - opens with Johann Sebastian Bach's "Air" from Orchestral Suite No. 3, BWV 1068.
(1989) "Dreaming (Tell Me) (live)" by Yngwie J. Malmsteen - opens with Johann Sebastian Bach's Fugue (the Little), BWV 578.
(1989) "Far Beyond the Sun (live)" by Yngwie J. Malmsteen - opens with a theme from Niccolò Paganini's "Allegro Maestoso" from Violin Concerto No. 4.
(1989) "Guitar Solo (live)" by Yngwie J. Malmsteen - breaks into the opening of Beethoven's 5th Symphony about halfway through the solo.
(1989) "Leningrad" by Billy Joel - quotes at length the song Waldesnacht, du wunderkühle by Johannes Brahms
(1989) "Rose of Pain" by X Japan - takes much of its melody from Johann Sebastian Bach's "Little Fugue" in G Minor
(1990) "Mea Culpa" by Enigma - based on the Gregorian chant "Kyrie Eleison"
(1990) "Operaa House!" by Malcolm McLaren and the World Famous Supreme Team - based on the "Flower Duet" from Léo Delibes' opera Lakmé
(1991) "World In Union" by Kiri Te Kanawa (official theme song of the Rugby Union World Cup) - based on "I Vow to Thee, My Country" from Holst's The Planets Suite, opus 32, Jupiter, Bringer of Jollity (also covered by Ladysmith Black Mambazo (1995) and Shirley Bassey/Bryn Terfel (1999))
(1991) "All Together Now" by The Farm based on Johann Pachelbel's Canon in D Major
(1992) "No Mercy" by Yngwie J. Malmsteen - breaks into Johann Sebastian Bach's "Badinerie" from Orchestral Suite No. 2, BWV 1067 right before the guitar solo.
(1994) "Basket Case" by Green Day - based on Johann Pachelbel's Canon in D Major
(1994) "Hook" by Blues Traveler - based on Johann Pachelbel's Canon in D Major
(1994) "Pictures at an Exhibition" by Tangerine Dream on Turn of the Tide - based on the "Promenade" section of Pictures at an Exhibition by Mussorgsky as arranged by Maurice Ravel for orchestra.
(1994) "Prisoner of Your Love" by Yngwie J. Malmsteen - chorus is based on Johann Sebastian Bach's "Air" from Orchestral Suite No. 3, BWV 1068.
(1995) "Clubbed to Death" [I] by Rob Dougan on Furious Angels - parts inspired by Edward Elgar's Enigma Variations
(1995) "Largo (from Xerxes)" by Tangerine Dream on Tyranny of Beauty - based on Haendel's Serse (alias Xerxes).
(1995) "Memory/Dead Winter Dead Intro" by Savatage - quoting Ludwig van Beethoven's Ode to Joy
(1995) "Overture 1622" by Yngwie J. Malmsteen - based on Wolfgang Amadeus Mozart's Symphony No. 25.
(1995) "Scatman's World" by Scatman John - based on Johann Pachelbel's Canon in D Major
(1996) "Clubbed to Death 2" [I] by Rob Dougan on Furious Angels - parts quoting Frédéric Chopin's "Prelude No. 4 in E minor" (in Preludes, opus 28)
(1996) "Paparazzi" by Xzibit - containing "Pavane" by Gabriel Fauré.
(1996) "Don't Look Back in Anger" by Oasis - chorus chord progression borrows from "Canon" by Pachelbel.
(1996) "A Mad Russian's Christmas" by Trans-Siberian Orchestra - Includes several passages from the "Swan Lake" by Pyotr Ilyich Tchaikovsky.
(1997) "Air on a Theme" by Yngwie J. Malmsteen - based on Antonio Vivaldi's "Largo" from Piccolo Concerto in C.
(1997) "C U When U Get There" by Coolio - containing Johann Pachelbel's Canon in D Major.
(1997) "Tubthumping" by Chumbawamba - quotes Jeremiah Clarke's Trumpet Voluntary.
(1997) "Lacrimosa" by Daddy Roach & Gimme - based on Mozart's Requiem.
(1998) "Everything's Gonna Be Alright" by Sweetbox - based on Johann Sebastian Bach, Air from the Orchestral Suite No. 3 in D major
(1999) "Arpeggios From Hell" reworked/renamed "Molto Arpeggiosa" by Yngwie J. Malmsteen - based on Beethoven's Piano sonata No. 14, "Moonlight", 3rd movement
(1999) "Barber's Adagio for Strings" by William Orbit - a techno/electronic version of Samuel Barber's "Adagio for Strings"
(1999) "Love of my Life" from Supernatural by Santana and Dave Matthews - based on the third movement from Johannes Brahms's Symphony No. 3
(2000) "Graduation (Friends Forever)" by Vitamin C - based on Johann Pachelbel's Canon in D Major
(2000) "Hall of the Mountain King" [I] by Apocalyptica - cello/metal cover of Edvard Grieg's Peer Gynt (Suite No.1, opus 46)
(2000) "Love U Crazay" by En Vogue from Masterpiece Theatre - set to Tchaikovsky's "Dance of the Sugar Plum Fairy" from Nutcracker
(2000) "Those Dogs" by En Vogue from Masterpiece Theatre - set to Bizet's "La Habañera" from Carmen.
(2000) "Sad But True" by En Vogue from Masterpiece Theatre - set to Beethoven's "Moonlight Sonata" or Piano Sonata No. 14 in C Sharp Minor, Op. 27 No. 2
(2000) "Prophet of Doom" by Yngwie J. Malmsteen - quotes themes from Niccolò Paganini's "No. 24" of the 24 Caprices.
(2001) "Black, Black Heart" by David Usher from Morning Orbit - containing Léo Delibes' "The Flower Duet" from Lakmé
(2001) "Coming 2 America" by Ludacris from Word of Mouf - containing Mozart's "Requiem", 3rd movement (Dies irae) and Antonin Dvorak's Symphony No. 9, "From the New World", 4th movement (Allegro con fuoco)
(2001) "Piano & I" by Alicia Keys - based on Beethoven's Piano sonata No. 14, "Moonlight", 1st movement
(2001) "Someone to Call My Lover" by Janet Jackson - uses Erik Satie's Gymnopedie No. 1 (as well as America's "Ventura Highway").
(2001) "Yatta" by Happa-tai - based on Johann Pachelbel's Canon in D Major
(2002) "I Can" by Nas - contains a sample of the classical piece Für Elise by Beethoven.
(2002) "Symphony in X Major" by Xzibit - based largely on a (minor key) section Johann Sebastian Bach's Third Brandenburg Concerto
(2003) "When I Get You Alone" by Thicke - based on a sample from Walter Murphy's "A Fifth of Beethoven" (q.v.) - itself based on Beethoven's Fifth Symphony
(2003) "If And When We Rise Again" by Streetlight Manifesto - contains a horn solo based on Johannes Brahms' Hungarian Dance No. 5 in G minor
(2003) "Karma" by Alicia Keys - contains a sample from Johannes Brahms' Violin Concerto
(2004) "Paris" by Delerium - based on Johann Pachelbel's Canon in D Major
(2005) "They" by Jem - largely based on Prelude 12 from J. S. Bach's The Well-tempered Clavier (Book 2)
(2005) "Road to Joy" by Bright Eyes is based on the melody of Beethoven's Ode to Joy