This was written in 1927 by songwriters Milton Ager and Jack Yellen, and it quickly became a standard. Ager wrote the lyrics for his daughter Shana, who later became an actress and political commentator named Shana Alexander.
This song was first recorded in 1927 as a piano tune by Frank Banta. Some of the many artists who recorded this include Frank Sinatra, Harry James, Lawrence Welk and Gene Vincent. (thanks, Terry - Willmar, MN)
The Beatles recorded this in June, 1961 in Hamburg, Germany. They played in German clubs 1960-1961, becoming much better musicians as a result.
John Lennon decided to play this "as a march," whereas the Gene Vincent version is much softer. A softer version can be heard on Anthology 3.
Most songs The Beatles covered were '50s R&B hits, but this was a 1927 pop hit that the fab four liked. (thanks, Loretta - Liverpool, England, for above 2)
Pete Best played drums on this. He earned some royalties when this was released on their Anthology album. It was one of the few times he benefited from The Beatles' success.
The Beatles didn't release this in the US until 1964, 3 years after it was recorded.