• Paul McCartney wrote this about his girlfriend, an actress named Jane Asher. They split for good in 1968.
• The Beatles recorded this specifically for release as a single at two quick sessions while they were making the Rubber Soul album in October 1965. When it was released as a single backed with "Day Tripper", debate raged over which was the A-side. Most pop groups put B-sides on their singles that were far inferior, but The Beatles often came out with 45s containing two great songs.
• A promotional film - one of the first music videos - was made to support this song. This was done in a shoot on November 23, 1965 at a film studio in London, where they recorded clips for four others songs as well. The Beatles did this so they could get their songs broadcast without actually appearing on the TV shows, clearing their schedules for other matters. They did three different version of "We Can Work It Out," all with John Lennon at the organ.
• The only time The Beatles played this live was on their final British tour in November/December 1965. McCartney didn't perform the song until 1991, when he played it on his 1991 MTV Unplugged appearance. On his 2002 Back In The US tour, McCartney played a solo version on his acoustic guitar.
• In many KUMON (reading and writing centers) in Canada, there are posters of Paul and at the bottom, it says "We Can Work It Out." 
• The single was number 1 in Britain (where it won the Ivor Novello Award for the top-selling A-side of 1965), America, Australia, Canada and Ireland.
• No record exists of the band members' exact contributions to the recording, leading to uncertainty regarding who's playing some of the instruments.

Thanks for reading!

CATW