Perhaps the most obvious example of American Imperialism was American actions during and immediately after the Spanish American War. The war itself began on a whim, and Spain's attempts to prevent it were thwarted by American desire for that which Secretary of State John Hay called a "splendid little war." Under the terms of the Treaty of Paris of 1898, the U.S. gained Puerto Rico and the Philippines, the first U.S. possessions outside the continental U.S. A pervading element of this imperialist action was to "Americanize" these countries as much as possible. The effort in the Philippines was best expressed by then President William McKinley:
It came to me late at night this way—I don’t know how it was, but it came. (1) that we should not give them back to Spain—that would be cowardly and dishonorable; (2) that we could not turn them over to France or Germany—our commercial rivals in the Orient—that would be bad business and discreditable; (3)that we could not leave them to themselves—they were unfit for self government—and they would soon have anarchy and misrule over there worse than Spain was, and (4) that there was nothing left for us to do but to take them all, and to educate The Filipinos, and uplift and civilize and Christianize them, and by God’s grace do the very best We could by them, as our fellowmen for whom Christ also died. And then I went to bed and slept soundly.
There was tremendous opposition to U.S. occupation of the Philippines, primarily by the American Anti-Imperialist League, whose members included Andrew Carnegie, Samuel Gompers, and Mark Twain. Their efforts to prevent annexation were ultimately unsuccessful.
A second and equally blatant example was the annexation of Hawaii, also not part of the Continental U.S. American sugar plantation owners there staged a revolt against Queen Liliuokolani, and the American minister there called in Marines to support the Americans. In a cable to Washington, he commented:
The Hawaiian pear is now fully ripe, and this is the golden hour for the United States to pluck it
Ultimately, on July 4, 1894, the Republic of Hawaii was proclaimed whose constitution contained a standing provision to seek annexation by the U.S. When the Japanese showed interest in annexing the Islands, President McKinley sent warships there, and asked the Senate to approve a Treaty of Annexation. He could not get the necessary 2/3 majority vote to approve the treaty, so a Joint Resolution of Congress (which only required a simply majority in both Houses) was passed, and Hawaii was annexed to the U.S. in 1898.
Though there is some debate as to whether they qualify as "imperialist" or not, the actions of the United States that can be identified as imperialist go back at least to the displacement of the American Indians along the frontier and even from the original colonies. The fact that European settlers used their advantages in military might and technology and the devastation wrought upon many Indian settlements by European diseases to take those territories and force Indians out certainly was an example of American Imperialism.
Others include, again with some debate, the Louisiana Purchase, the Mexican War, the Spanish American War, and even American interventions in various places after World War II, especially those that included the installation of pro-U.S. governments. Korea, Vietnam, even Iraq and Afghanistan are considered by many as further examples of American Imperialism.