House Of The Rising Sun.
Credence Clearwater Revival recorded Midnight Special in 1969.
Eric Clapton recorded Robert Johnson’s “Crossroads Blues” in the same year.
Sting had a UK hit with “Spread a Little Happiness”, from a 1929 musical.
I’m not sure that songs based, to varying degrees, on classical tunes are what the OP is after. But if so, there’s also:
“Could It Be Magic” - Barry Manilow (Chopin: Prelude in C minor)
“A Groovy Kind Of Love” - Phil Collins (Clementi: Sonatine in G)
“All Together Now” - The Farm (Pachelbel: Canon)
“Song Sung Blue” - Neil Diamond (Mozart: Piano Concerto No. 21, second movement)
“Russians” - Sting (Prokofiev: Lieutenant Kijé)
and the possibly accidental similarity of Strawberry Switchblade’s “Since Yesterday” to part of Sibelius’s Symphony no.5. Then there’s the Beatles’ “Because”, supposedly inspired by reversing the chords of Beethoven’s Moonlight Sonata.
Not sure if any of these were hits, but Wikipedia shows the following artists have recorded “Greensleeves” (1580):
Odetta: 1957 album At the Gate of Horn
John Coltrane: 1961 album Africa/Brass
Vince Guaraldi Trio: 1965 soundtrack A Charlie Brown Christmas
Elvis Presley: 1968 retitled as “Stay Away” B-side of “U.S. Male”; featured in film Stay Away, Joe
James Taylor: 1968 debut album James Taylor
Jeff Beck: 1968 album Truth
Glen Campbell: 1972 album The Artistry of Glen Campbell
Leonard Cohen: 1974 album New Skin for the Old Ceremony
Flanders and Swann: The Greensleeves Monologue Annotated
Olivia Newton-John: 1976 album Come on Over
Mason Williams with Mannheim Steamroller: 1987 album Classical Gas
Loreena McKennitt: 1991 album The Visit
Timo Tolkki: 1994 album Classical Variations and Themes
Blackmore’s Night: 1997 debut album Shadow of the Moon
Vanessa Carlton: 2002 album Maybe This Christmas
Ensemble Planeta: 2003 album étoile
Jethro Tull: 2003 album The Jethro Tull Christmas Album
David Nevue: 2004 album Sweet Dreams and Starlight
Kevin Max: 2005 album Holy Night
Derek Trucks Band: 2006 DVD Songlines Live
The King’s Singers: 2008 album Simple Gifts
Daniel Kobialka: “Greensleeves Fantasy”; 2009 album Musical Inspirations Series: Peace
Paul McCartney wrote the tune, but the lyrics to “Golden Slumbers” are taken from a poem by Thomas Dekker written in the 1600s.
Also, Nut Rocker
Bryan Ferry had a minor 1974 hit with “Smoke Gets in Your Eyes,” by Jerome Kern from the 1933 musical Roberta. Also famously recorded by The Platters in the late fifties, but I don’t know if you’d consider them ‘rock’. (Similarly, does Bobby Darrin’s huge recording of the Brecht/Weill 1929 song “Mack the Knife” count as rock? Certainly pop.)
NDP mentioned Traffic’s version of “John Barleycorn Must Die”, which was also done by Jethro Tull on their album “A Little Light Music” (very good version, btw).
Then, of course, there’s Emerson, Lake, and Palmer, who used lots of classical music references in their work (not to mention pre-ELP Emerson when he played with The Nice…as well, now that I think of it…as second generation-ELP Emerson who did “Mars, the Bringer of War” on the Emerson, Lake, and Powell album).
Also, a sort of German version of ELP called Triumvirat started out with a suite based on excerpts from Motzart.
My favorite: “Powerhouse” by Raymond Scott co-opted by Alex Lifeson and riffed on in the classic RUSH instrumental “La Villa Strangiato.”
Spelled “Mozart”, but pronounced “Throatwarbler Mangrove.”
“Just A Gigolo”, a big hit for David Lee Roth in the mid-1980s, was a pretty faithful cover of Louis Prima’s recording of it (including pairing it with “Ain’t Got Nobody”) from 1956, which was itself an innovative cover in its own time of the 1929 song, which was a Tin Pan Alley translation into English of the original Austrian song (in German).
Jimi Hendrix’s rendition of The Star-Spangled Banner may not have been a chart hit, but it was certainly iconic. The tune was taken from The Anacreontic Song, written in the late 1770s.
I’m sure you meant the second movement.
It wasn’t a hit, unfortuneately, but the Doors covered “The Whiskey Song” by Weill/Brecht.
It’s my understanding that the Four Seasons hit “Oh, What a Night” was originally about the repeal of Prohibition in 1933; someone just changed some of the lyrics.
And Carmen’s “Never Gonna Fall in Love Again” is an adaptation of the adagio of Rachmaninoff’s Symphony #2.
Both Willie Nelson and Ray Charles had hits with Georgia on My Mind (1930).
“Mule Skinner Blues”, originally “Blue Yodel #8” by Jimmie Rodgers (1930), was a #5 hit for the Fendermen in 1960.
The tune of Dan Fogelberg’s “Same Old Lang Syne” is Tchaikovsky’s “1812 Overture, Op. 49” (1880) played downtempo.
Also, Jethro Tull’s instrumental “Bouree” is a modern interpretation of J.S. Bach’s “Suite in E minor for Lute” (fifth movement).
Herman’s Hermits also had a #7 hit with “Leaning on a Lamp Post”, originally performed by George Formby Jr. in “Me and My Girl” 1937.
There’s also Weill’s September Song.
Can’t Help Falling in Love (a hit for Elvis) was based on the French song Plaisir d’Amour, which was written in 1780.