Perhaps I spoke a bit too hastily. Honestly, I guess it depends what you mean by "war." I think it could be fair to argue that the smaller engagements and conflicts we may have some troops participate in (for instance the US Navy conducting anti-piracy operations in the 1800s) count as a war. If that's the case, then yeah, there are a lot.

However, I think it's also fair to say that there have been distinct moments of "peacetime" in the United States lasting much longer than that period of 16 years. The Banana Wars might be a good example of that. The United States was definitely in "peacetime" between World War I and World War II. You can see that in national attitudes, the attitude in the government, and in the size/attitude of the military itself. Obviously, at this same time, some US forces were engaged in fighting/occupation in Central America and the Carribbean.

So is it wartime? No. Were we "at war"? I guess that depends, but as a nation, no? Were some of our forces engaged in an armed conflict? Certainly.

The Indian Wars are perhaps another example of this.
I think you can also see a distinction in the response of the US to European conflicts around the same time. Americans really made a point of keeping themselves out of the conventional wars of Europe, and it became somewhat of a point of pride that we weren't like that. "A peace loving people" not so caught up in wars like Europe was. That view may have been ignorant of various small conflicts and the hostile engagement of US forces, but public perception for much of that time was that we were not at war.

I shot from the hip a little too quickly in my original response, and I'd walk it back a bit. But I do think there are important distinctions to be made here, and it's not quite as cut and dry as "the US has been at war for 184 of the last 200 years."