Oooh tough call, but I'm probably gonna have to cheat and go with two.. 'Hey Jude' and 'Yesterday'.
Hey Jude will always be a favourite of mine because I have seen (not personally unfortunately) McCartney end many shows with it and to see the reactions of the audiences as they sing along is just amazing.
'Yesterday' is a song I grew up with thanks to my Dad. He's 69 and grew up on Merseyside, home of the Beatles. He grew up listening to their music and in turn, I listened to it too. I used to hear the song on the radio all the time and even when I was feeling happy, or sad, I would always be able to find myself singing along.
If forced to make a choice between the two songs, Yesterday would be my ultimate pick..my favourite Beatles song and just one of those tracks I think everyone needs to hear at least once.