1964 followed by 1965
April
April 4 – The Beatles hold the top 5 positions in the Billboard Top 40 singles in the United States, an unprecedented achievement. The top songs in America as listed on April 4, in order, are: "Can't Buy Me Love", "Twist and Shout", "She Loves You", "I Want to Hold Your Hand", and "Please Please Me".
April 7 – IBM announces the System/360 computer.April 8 – The U.S. Gemini 1 is launched, the first unmanned test of the 2-man spacecraft.
April 9 – The United Nations Security Council adopts by a 9–0 vote a resolution deploring a British air attack on a fort in Yemen 12 days earlier, in which 25 persons have been reported killed.
April 11 – The Brazilian Congress elects Field Marshal Humberto de Alencar Castelo Branco as President of Brazil.
April 13 – At the 36th Academy Awards ceremony, Sidney Poitier becomes the first African-American to win an Academy Award in the category Best Actor in a Leading Role in Lilies of the Field.
April 16 – In the Assize Court at Buckingham in England, sentences totalling 307 years are passed on twelve men who stole £2,600,000 in used bank notes, after holding up the night train from Glasgow to London in August 1963 – a heist that becomes known as the Great Train Robbery.
April 19 – In Laos, the coalition government of Prince Souvanna Phouma is deposed by a right-wing military group, led by Brig. Gen. Kouprasith Abhay. Not supported by the United States, the coup is ultimately unsuccessful, and Souvanna Phouma is reinstated, remaining as Prime Minister until 1975.
April 20
U.S. President Lyndon Johnson in New York, and Soviet Premier Nikita Khrushchev in Moscow, simultaneously announce plans to cut back production of materials for making nuclear weapons.
Nelson Mandela makes his "I Am Prepared to Die" speech at the opening of the Rivonia Trial, a key event for the anti-apartheid movement.
In the UK, BBC Two television starts broadcasting for the first time.
April 22British businessman Greville Wynne, imprisoned in Moscow since 1963 for spying, is exchanged for Soviet spy Gordon Lonsdale.
The 1964 New York World's Fair opens to celebrate the 300th anniversary of New Amsterdam being taken over by British forces under the Duke of York (later King James II) and being renamed New York in 1664. The fair runs until October 18, 1964, and reopens April 21, 1965, finally closing October 17, 1965. Although not internationally sanctioned, due to being within ten years of the Seattle World's Fair in 1962, so that some countries decline to attend, many have pavilions with exotic crafts, art and food.
April 25 – Thieves steal the head of the Little Mermaid statue in Copenhagen, Denmark. Although the attack is attributed to Jørgen Nash, the Danish media blame painter Henrik Bruun, who never confesses to the crime).
April 26 – Tanganyika and Zanzibar merge to form Tanzania.