What were the results of America's 19th century imperialism?
I'll talk about two sorts of results.
The first, and most obvious, result was that the United States obtained a sort of empire that gave it a presence over a huge area of the Pacific (and the Caribbean as well). The US presence extended all the way to the Philippines.
The second impact of this was that American imperialism led to complications in dealing with other countries. The most prominent example of this was WWII. You can argue that if the US had not taken its Pacific Empire (notably the Philippines and to some extent Guam), Japan would never have attacked Pearl Harbor. This is not to say that Pearl Harbor was our fault, but it is to say that Japan would have had no reason to worry about the US if our territory ended on the West Coast (or even, likely, if it ended at Hawaii).
Instead, by extending our reach, we put ourselves into areas that would become the subject of conflict. We involved ourselves in more areas of the world than we would otherwise have been involved in and this, at times, led to problems for us.