Americans after October 1962 believed that the Soviet Union had equalled the United States' nuclear capability.  The immediate effects were that missiles were withdrawn from Cuba, and the United States secretly agreed to withdraw its missiles from Turkey.  By June 1963 the first telephone "hotline" was installed for the leaders of the superpowers to directly communicate.  The primary longer term effect began in August 1963, when both Soviet Union and United States formally began the long process of detente, both sides having been frightened into how easily thermonuclear war could ignite.

One of the effects of the Cuban Missile Crisis was to test or prove the diplomacy and bargaining powers of both Kruschev and Kennedy. The (outdated) missiles in Turkey for the removal of the missiles in Cuba.

A second effect of the Cuban Missile Crisis was to continue the spy sattelite programs because of the effectiveness of the surveillance and proof positive that missiles were on the bases in Cuba. The space was serious and in earnest.  The efforts to use spy cameras in space and on airplanes gained momentum.

Finally, because neither side in the Cuban Missile Crisis had absolute assurance that the thing would not escalate into a shooting war, the leaders had to establish trust through secret deals and assurances. This may or may not have undermined the public trust, but it did avert impending doom and nuclear war.

One of the effects of the crisis was to terrify the population of the United States and to increase paranoia and help support the willingness of Americans to spend huge amounts of money on defense and to continue the massive arms race with the Soviets.

Another effect was to actually build some greater ability to negotiate and communicate between the two powers as they found ways to use back channels to avoid an actual shooting war.

In some ways the crisis was used very well by Kennedy to make himself look good and tough.