Partial list of songs that use the I—vi—IV—V or I—vi—ii—V chord progression as their harmonic basis

Heart and Soul (Carmichael and Loesser)
Stand by Me (Ben E. King)
Blue Moon (Rodgers and Hart)
Earth Angel (Williams, Belvin, and Hodge)
Stand By Me (Ben E. King)
Duke of Earl (Gene Chandler)
Loveable (Sam Cooke)
Jesus of Suburbia (Armstrong, Dirnt, and Cool)
In the Aeroplane Over the Sea (Neutral Milk Hotel; Mangum)
Eternal Flame (Hoffs, Kelly, and Steinberg)
True Blue (Madonna)
Perfect (Ed Sheeran)
Bristol Stomp (The Dovells; Mann, and Appell)
Stir It Up (Bob Marley)
Beauty School Dropout (Jacobs and Casey)
Since I Fell For You (Buddy Johnson)
These Foolish Things (Strachey and Maschwitz)
Hallelujah (Leonard Cohen)
Every Breath You Take (Sting)
Sherry (The Four Seasons; Bob Gaudio)
Carolina In My Mind (End of choruses; James Taylor)
Baby (Justin Bieber, Christopher Stewart, Terius Nash, Christopher Bridges, Christina Milian)
D’yer Mak’er (Led Zeppelin; Bonham, Jones, Page, Plant)
Marvin Gaye (the song) (Charlie Puth, Julie Frost, Jacob, Luttrell, Nick Seeley)
Dear Future Husband (Meghan Trainor, Kevin Kadish)
All I Have to Do Is Dream (The Everly Brothers; Boudleaux Bryant)
Runaround Sue (Dion DiMucci, Ernie Maresca)

Special thanks to songwriters Jimmy Clark (http://JCMusicAndWellness.Com) , John Primerano (http://www.johnprimerano.com), and Herbert Roselle for their assistance in assembling this list.

For examples from concert music literature that use the progression, visit https://en.wikipedia.org/wiki/50s_progression