It's generally accepted that the most performed song in the world is "Happy Birthday To You", and the most commonly reproduced by mechanical means is that Holst tune played by chiming clocks the world over.
As for most popular, who knows? Though there has been a poll running on the BBC World website. I haven't seen it myself but a search on BBCi should turn up the results to date.
Well, at the end of 1999, I think it was VH1 that did a big survey to find out which song was voted the Number 1 song over the last century (as we were going into the 21st Century and all that.) Can't remember what was second and third, but John Lennon's Imagine was number 1.
Imagine? - In UK maybe, though actually it's 'English Rose' but worldwide? and not counting Happy Birthday? - Maybe 'Silent Night' or that one by Slade.