I'm talking about everything from the Indian Wars to the 2011 Libyan Intervention. Correct me if I'm wrong because I'm not sure if these particular engagements count as wars, but I'd imagine that some form of declaration of war has been written down somewhere. Thanks for the help in advance! I'm trying to justify what constitutes a "war."
True declarations of war are few, in United States history. If you go by pure declarations, the US has only been involved in:
War of 1812 (with the UK).
Mexican-American War (1846).
Spanish-American War (1896).
World War I (1917), Germany And Austria specifically.
World War II (1941-42), Japan, Germany, Italy in 1941 and Romania and Hungary added in 1942.
This, obviously doesn't cover most of what the United States has done militarily. There have been instances of war that do not fall under a formal declaration, but which were authorized by Congress. Notable examples are Vietnam and the Gulf War, and even the war in Iraq.
If you want to go through every military fight that the US has been involved in, that doesn't have a formal declaration, there's quite a few. Wikipedia does a decent job of listing them.
However, if you want to know what qualifies as a war as a defining matter, you'd do best to look to various political theorists along with international bodies, like the UN and League of Nations. Some recommended theorists include Charles R. Beitz, Michael Walzer, and John Rawls. All talk extensively about the right to go to war, what qualifies as a just war, and what war essentially is. UN definitions of war are also fairly clear. How many wars the US has been in, I can't really count; I don't have that extensive an education just yet. US intervention has been pretty proliferated (that's not to say it's worse or better than other interventions by other powers, or anything, just that it has been numerous), and you'd be hard-pressed to find a fully-functioning definition of war that applies to everything properly and with everyone in agreement.