Don't forget John Lennon.
Lennon–McCartney (sometimes McCartney–Lennon) were a brilliant team!
Lennon–McCartney (sometimes McCartney–Lennon) was a songwriting partnership.
They are the best known and most successful musical collaboration ever by records sold, with the Beatles selling over 600 million records worldwide as of 2004. Between 5 October 1962 and 8 May 1970, the partnership published approximately 180 jointly credited songs, of which the vast majority were recorded by the Beatles, forming the bulk of their catalogue.
Unlike many songwriting partnerships that comprise a separate lyricist and composer, such as Jerry Leiber and Mike Stoller, Rodgers and Hammerstein, Hal David and Burt Bacharach or Elton John and Bernie Taupin, both Lennon and McCartney wrote lyrics and music. Sometimes, especially early on, they would collaborate extensively when writing songs, working "eyeball to eyeball" as Lennon phrased.
After this brilliant team split up, I felt the music they wrote that followed, was not as good as when they were a team.