Because I do not know what time period you want the effects to come from, I will discuss three effects of the US intervention in the Cuban rebellion against Spain. Two effects were rather immediate, while the third came decades later.
The first effect of the American intervention was to free Cuba from Spain. Without US intervention, it is unlikely that the Cuban rebels would have been able to defeat the Spanish forces in Cuba. When the US intervened, it was able to defeat Spain rather decisively, allowing Cuba to become an independent country.
A second impact of American involvement was to help make the United States an imperial power. Before its intervention in Cuba, the US had very little influence over any territory outside of North America. With the Spanish-American War, that changed. The US did not take Cuba, but (through the Platt Amendment) it essentially controlled that island. It did take possession of Puerto Rico, Guam, and the Philippines. During the war (though not related to the war directly) it annexed Hawaii. Thus, intervention in Cuba put the US on the road to being a world power.
Finally, the US intervention in Cuba helped to bring about the Cuban Revolution of 1959 and the enduring enmity between the two countries after that revolution. After Cuba gained its independence, the US had great influence over the island and its government. When Fidel Castro and his communists opposed Fulgencio Batista, the US saw it as opposition to American interests. Because of this, the US opposed Castro and Castro threw in his lot with the Soviet Union. This helped bring about the bad relations between the two countries that have endured to the present. Had the US not taken control of Cuba after intervening in its revolution, things might have been very different.