I once did a series of cassette mixes called "Doubles" of different songs with the same title, including more contemporary material than this Forum usually deals with:
"Liza": George Gershwin's song and the one recorded by McKenzie's and Condon's Chicgoans in 1927.
"Oh, Baby": With Bix and the Wolverines, and the "Rise and Shine" song recorded by Frank Teschemacher in 1929 and Benny Goodman in 1946.
"Pretty Woman": Duke Ellington, Otis Rush (covered by John Mayall), and Roy Orbison.
"What Goes On?": The Beatles and The Velvet Underground.
"Run, Run, Run": The Velvet Underground and Yoko Ono.
"One Day at a Time": The theme from the 1970's TV show and an original by John Lennon.
And probably the weirdest mismatch: "Stairway to Heaven" by Neil Sedaka and Led Zeppelin.