The U.S. is a weird sort of quasi-empire with military outposts and large economic interests all over the world, but in territories that aren't their own and with the notion that the countries we inhabit are not part of the U.S. in any way shape or form. Sort of like vassal states, but without all the "pay us your tribute or we'll invade and burn your cities down" that modern America is terribly uncomfortable with.
It's an interesting academic exercise to pick apart where the U.S. is and isn't like an Empire because it's not that simple.
And here's a graphic from 1898 which proudly shows the US eagle dominating an entire side of the globe, from the Philippines to Puerto Rico.
http://en.wikipedia.org/wiki/File:10kMiles.JPG
I know you mentioned the Phillipines and Puerto Rico already, but what's striking is that you somehow think it doesn't count as a real empire. But there's no inherent reason why the USA should have such a large sphere of influence, other than it can. There's not even any inherent reason why it had to dominate all the land west of the original colonies, wresting it not only from native Americans but other colonial powers.
For most of its history the USA was proud to say it was building an empire and dominating other nations (for their own good, of course!). I'm not sure when this propaganda effort started that there is no American empire -- perhaps the US wanted to assert it was more pro-local-sovereignty than other competing empires, like the USSR.
The continental US west of the original colonies was an interesting case. We only got the bulk of it because Napoleon put the entire Louisiana Territory on fire sale--he wanted to cut his losses in America after losing Haiti and needed the money to try and conquer Europe. We only really wanted the Mississippi River delta to begin with. We did kind of pick a fight with Mexico, but we didn't conquer the whole country, and even paid for the parts we took. Oregon was a disputed claim and we split it down the middle with the British. And Alaska we paid for fair and square. As for the American Indians, you have a point there but frankly smallpox had already depopulated the continent and it was practically empty. If it wasn't, I don't think anyone would have been able to conquer America from the American Indians--nor would any colonial power.
When people call the US an empire, they usually aren't thinking about the Spanish-American War. They're thinking about all the countries we station troops in (most of them asked us to), or all the Coca-Cola we sell (which the world voluntarily buys). We have a big sphere of influence because not too long ago, the world needed us to. We were the only democratic allied power left largely untouched by WWII, and our "imperialism" at the time consisted largely of a Marshall Plan designed to rebuild a continent that destroyed itself twice over, both times somehow roping us into the action.
Can you honestly think of a country the US has dominated against its will since the Philippines? You might be able to make a case for South Vietnam, and you could name maybe a dozen countries we covertly subverted, but outright domination? We didn't hold a candle to the Soviets.
There are many countries where the US has toppled one government for another, or propped up a leader the populace didn't like.
That's where most of the criticism comes from.
Oh yeah, we helped set up a leader friendly to the cause of righteousness, supplied him with advisors, gave him weapons or gave him access to buy them, ensured that he was friendly to exporting the mineral/oil/food wealth of his country via our companies and institutions, shared intelligence about his adversaries, installed a military base and ensured we had the right to conduct our wars using his territory.... but it's not like we took over the country! We are the friends of the common people!
People who say the US was imperialistic seem to forget that we didn't, for example, send tanks into France when they wanted to pull out of NATO, which is more than you can say about the other superpower. The British empire stationed troops and bureaucrats all over the world where they weren't wanted. They directly ruled over civilizations larger and more ancient than their own. Aside from the Philippines (whom we granted independence in 1946) and Hawaii and Puerto Rico (who both want to stay with us), we didn't really do that. It starts getting far more abstract when you talk about American imperialism via Coca-Cola and blue jeans.