August 2 – United States destroyer Maddox is attacked in the Gulf of Tonkin. Air support from the carrier USS Ticonderoga sinks one gunboat, while the other two leave the battle.

August 5 - Operation Pierce Arrow – Aircraft from carriers USS Ticonderoga and USS Constellation bomb North Vietnam in retaliation for strikes against U.S. destroyers in the Gulf of Tonkin. The Simba rebel army in the Democratic Republic of the Congo captures Stanleyville, and takes 1,000 Western hostages.

August 7 – The United States Congress passes the Gulf of Tonkin Resolution, giving U.S. President Lyndon B. Johnson broad war powers to deal with North Vietnamese attacks on U.S. forces.

August 8 – A Rolling Stones gig in Scheveningen gets out of control. Riot police end the gig after about fifteen minutes, upon which spectators start to fight the riot police.

August 13 – The last judicial hanging in the United Kingdom takes place when murderers Gwynne Owen Evans and Peter Anthony Allen are executed at Walton Prison in Liverpool.

August 16 – In a coup, General Nguyễn Khánh replaces Dương Văn Minh as South Vietnam's chief of state and establishes a new constitution, drafted partly by the U.S. Embassy.

August 18 – The International Olympic Committee bans South Africa from the Tokyo Olympics on the grounds that its teams are racially segregated.

August 20 – The International Telecommunications Satellite Consortium (Intelsat) began to work.

August 22 – Goalkeeper Derek Foster of Sunderland becomes the youngest-ever player to play in the English Football League, aged 15 years and 185 days.

August 24 – The Democratic National Convention in Atlantic City nominates incumbent President Lyndon B. Johnson for a full term, and U.S. Senator Hubert Humphrey of Minnesota as his running mate.

August 27 – Walt Disney's Mary Poppins has its world premiere in Los Angeles. It will go on to become Disney's biggest moneymaker, and winner of 5 Academy Awards, including a Best Actress for Julie Andrews. It is the first Disney film to be nominated for Best Picture.

August 28 – Philadelphia 1964 race riot: Tensions between African American residents and police lead to 341 injuries and 774 arrests. (source: Wikipedia)