The Spanish-American War did not have very many major events as it was a rather short war. There are three events that were (more or less) part of this war that are famous in American history.
The first of these was not an actual event from the war itself. Instead, it was a cause of the war. This was the explosion of the USS Maine in Havana harbor. The US blamed it on the Spanish, helping to bring the war about.
Within the war, the most famous land battle was fought on Cuba. This was the battle in which the US attacked San Juan Heights. The attacks on Kettle Hill and San Juan Hill are famous because they helped make Theodore Roosevelt a major national figure. This battle was the only major land engagement on Cuba.
At sea, the most famous battle was the US attack on Manila Bay in the Philippines. This was a very one-sided battle in which only 9 Americans were wounded. This allowed the US to take control of the Philippines from Spain. There followed a long fight against Filipinos who wanted to become independent, but this is not typically seen as part of the Spanish-American War.