Great one @cd318! I have "Johnny Angel" on a 7" 45 (one of my first), and again fall in love with Shelley every time I hear it.
From roughly the same time---and also performed on the TV show he was appearing in at the time of it’s release---is "Young World" by Ricky Nelson. This perfect Pop song also contains a perfect guitar solo by the great James Burton, the obvious model for George Harrison’s solo in "Nowhere Man". Compare the two.
Also from the early-60’s are the amazing run of hits from Roy Orbison, including his biggest, "Oh, Pretty Woman". Best use of an Orbison song in a movie: the scene in Blue Velvet in which Frank (played to creepy perfection by Dean Stockwell) lipsynchs to "In Dreams". VERY disturbing.
The Everly Brothers also had an incredible string of perfect Pop song hits, most written by the husband-and-wife team of Felice & Boudleaux Bryant. "Bye Bye Love", "Wake Up Little Susie", "All I Have To Do Is Dream", "When Will I Be Loved" (already mentioned above), "Let It Be Me" (done by Dylan for his Self Portrait album), "Cathy's Clown", and "Love Hurts" (recorded by Gram Parson and Emmylou Harris for Gram's Grievous Angel. Good, but the Brothers' version is great).