In Farnam Street, one of my favorite blogs there is a comprehensive description of Butterfly Effect  the-butterfly-effect 

Below is a brief Extract of the last section of the same, which cites a few examples & Concludes 

Many examples exist of instances where a tiny detail led to a dramatic change. In each case, the world we live in could be different if the situation had been reversed. Here are some examples of how the butterfly effect has shaped our lives.

• The bombing of Nagasaki. The US initially intended to bomb the Japanese city of Kuroko, with the munitions factory as a target. On the day the US planned to attack, cloudy weather conditions prevented the factory from being seen by military personnel as they flew overhead. The airplane passed over the city three times before the pilots gave up. Locals huddled in shelters heard the hum of the airplane preparing to drop the nuclear bomb and prepared for their destruction. Except Kuroko was never bombed. Military personnel decided on Nagasaki as the target due to improved visibility. The implications of that split-second decision were monumental. We cannot even begin to comprehend how different history might have been if that day had not been cloudy. Kuroko is sometimes referred to as the luckiest city in Japan, and those who lived there during the war are still shaken by the near miss.
• The Academy of Fine Arts in Vienna rejecting Adolf Hitler’s application, twice. In the early 1900s, a young Hitler applied for art school and was rejected, possibly by a Jewish professor. By his own estimation and that of scholars, this rejection went on to shape his metamorphosis from a bohemian aspiring artist into the human manifestation of evil. We can only speculate as to how history would have been different. But it is safe to assume that a great deal of tragedy could have been avoided if Hitler had applied himself to watercolors, not to genocide.
• The assassination of Archduke Franz Ferdinand. A little-known fact about the event considered to be the catalyst for both world wars is that it almost didn’t happen. On the 28th of June, 1914, a teenage Bosnian-Serb named Gavrilo Princip went to Sarajevo with two other nationalists in order to assassinate the Archduke. The initial assassination attempt failed; a bomb or grenade exploded beneath the car behind the Archduke’s and wounded its occupants. The route was supposed to have been changed after that, but the Archduke’s driver didn’t get the message. Had he actually taken the alternate route, Princip would not have been on the same street as the car and would not have had the chance to shoot the Archduke and his wife that day. Were it not for a failure of communication, both world wars might never have happened.
• The Chernobyl disaster. In 1986, a test at the Chernobyl nuclear plant went awry and released 400 times the radiation produced by the bombing of Hiroshima. One hundred fifteen thousand people were evacuated from the area, with many deaths and birth defects resulting from the radiation. Even today, some areas remain too dangerous to visit. However, it could have been much worse. After the initial explosion, three plant workers volunteered to turn off the underwater valves to prevent a second explosion. It has long been believed that the trio died as a result, although there is now some evidence this may not have been the case. Regardless, diving into a dark basement flooded with radioactive water was a heroic act. Had they failed to turn off the valve, half of Europe would have been destroyed and rendered uninhabitable for half a million years. Russia, Ukraine, and Kiev also would have become unfit for human habitation. Whether they lived or not, the three men—Alexei Ananenko, Valeri Bezpalov and Boris Baranov—stilled the wings of a deadly butterfly. Indeed, the entire Chernobyl disaster was the result of poor design and the ineptitude of staff. The long-term result (in addition to the impact on residents of the area) was a widespread anxiety towards nuclear plants and bias against nuclear power, leading to a preference for fossil fuels. Some people have speculated that Chernobyl is responsible for the acceleration of global warming, as countries became unduly slow to adopt nuclear power.
• The Cuban Missile Crisis. We all may owe our lives to a single Russian Navy officer named Vasili Arkhipov, who has been called “the man who saved the world.” During the Cuban Missile Crisis, Arkhipov was stationed on a nuclear-armed submarine near Cuba. American aircraft and ships began using depth charges to signal the submarine that it should surface so it could be identified. With the submarine submerged too deep to monitor radio signals, the crew had no idea what was going on in the world above. The captain, Savitsky, decided the signal meant that war had broken out and he prepared to launch a nuclear torpedo. Everyone agreed with him—except Arkhipov. Had the torpedo launched, nuclear clouds would have hit Moscow, London, East Anglia and Germany, before wiping out half of the British population. The result could have been a worldwide nuclear holocaust, as countries retaliated and the conflict spread. Yet within an overheated underwater room, Arkhipov exercised his veto power and prevented a launch. Without the courage of one man, our world could be unimaginably different.

From these handful of examples, it is clear how fragile the world is, and how dire the effects of tiny events can be on starting conditions.

We like to think we can predict the future and exercise a degree of control over powerful systems such as the weather and the economy. Yet the butterfly effect shows that we cannot. The systems around us are chaotic and entropic, prone to sudden change. For some kinds of systems, we can try to create favorable starting conditions and be mindful of the kinds of catalysts that might act on those conditions – but that’s as far as our power extends. If we think that we can identify every catalyst and control or predict outcomes, we are only setting ourselves up for a fall.