When you ask about the “lasting effect” of the Cuban Missile Crisis, it implies that you are looking for effects that continue to be felt today. It is not at all clear that such effects exist. We cannot point with certainty to any particular phenomenon and know that it would not have existed without the crisis. If we have to identify an effect, though, I would say that the Cuban Missile Crisis helped to make the great powers afraid of direct confrontations with one another.
The Cuban Missile Crisis is commonly said to be the closest that the world has ever come to nuclear war. Poor decisions on the parts of both the US and the USSR led to a situation where fighting could easily have broken out. That fighting could have escalated to the point where nuclear weapons were used.
In the 50+ years since the Cuban Missile Crisis, great powers have been careful to avoid situations where they might get involved in direct confrontations. They have been careful to use proxies when they fight one another. They have also tried to avoid overt actions in places where conflict could arise between them. For example, neither the United States nor Russia has been willing to act openly on either side of the civil war in Ukraine. This reticence can be seen as the lasting effect of the Cuban Missile Crisis.