January 1:
The Beatles audition for Dick Rowe, head of Decca in London, by performing basically their entire club act of some twenty songs. They're turned down, a few days later, with Rowe delivering one of the most wrongheaded statements in recording history: "Guitar groups are on the way out, Mr. Epstein." 

March 8:
The Beatles make their first appearance on the BBC radio program "Teenagers' Turn".

April 10:
Stuart Sutcliffe dies of a brain hemorrhage in Hamburg.

June 6:
The group auditions successfully for EMI (Parlophone) record producer George Martin and gets signed up. (Martin will remain their producer throughout the Beatles' career.)

August 16:
On the urging of George Martin, drummer Pete Best is fired.

August 18:
Ringo Starr (who has been sitting in with the band occasionally when Pete Best was out sick) formally joins the Beatles.

August 23:
John Lennon and Cynthia Powell (pregnant with their child) get married in a 5 minute civil ceremony at Mount Pleasant Registry Office in Liverpool. George Harrison, Paul McCartney, Brian Epstein and Tony Powell attend.
(There is no public announcement and no formal wedding.)

September 11:
The Beatles record "Love Me Do" at Abbey Road, Studio
No.2. (John Lennon plays the harmonica.)

October 5:
"Love Me Do"/"P.S.I Love You" on Parlophone , the Beatles first single, is released in the U.K.  It quickly rises to # 17 on the British charts. (It's been said that Brian Epstein bought up 10,000 records to ensure the rating.)

October 17:
Pre-recorded at the Cavern, the Beatles' first TV appearance airs on Granada Television's "People and Places".

December 17:
The band travels to Germany for their final engagement in Hamburg at the Star Club.