On April 26, 1937, the German Luftwaffe (Condor Legion) bombed the Spanish city of Guernica during the Spanish Civil War. The Germans were attacking to support the efforts of Francisco Franco to overturn the Spanish Republican government. This act caused world-wide revulsion, but was only a taste of things to come.
The United Kingdom and the United States used fire-bomb attacks on Dresden during February 13-15, 1945, creating a firestorm which together with the bombing itself killed 135,000 citizens. The US bombing of Tokyo killed 83,000 citizens and the nuclear weapon attacks on Hiroshima killed 70,000 citizens and Nagasaki killed 36,000 citizens during World War II.
Some argue that these acts qualify as state terrorism. Others state that there were valid military reasons for the attacks on these particular locations. For example, Nagasaki had major naval shipyard facilities and Hiroshima had bases where tens of thousands of Japanese soldiers were quartered. There is also evidence that the United States attempted to repeatedly warn the civilian populations of Nagasaki and Hiroshima to evacuate the target areas. There is no evidence that killing civilians was the purpose and objective of the attacks.
During the Cold War, the threat of nuclear destruction of cities by ICBMs became the main instrument of the balance of terror that kept the United States and Soviet Union from open warfare with one another.
The United States has since bombed cities in other countries on a number of occasions, specifically Tripoli and Baghdad. These attacks have used "precision bombing" using smart bombs and non-nuclear cruise missiles.
See strategic bombing for a more thorough treatment of this subject.