Although I can pinpoint quite a few memorial sites and monuments I've visited in different parts of the world, my city even, those in the United States have impressed me the most.
There seems to be an attitude, a cultural trait, an inclination to the action of remembering the dead that I can't quite make my own. Some memorials somehow felt like an apology, sometimes like an explanation. Sometimes I felt the memorial created causality rather than remarking or celebrating it. Because there is a memorial that we (whatever "we" means) are what we are (free, happy, able to settle here, etc.). Sometimes it's only the circumstance of death, an inevitable fact of life, that makes a person deserving of having his or her name etched in stone - this person died because of a tragic event beyond her will or control.
Some tragedies beyond our will or control deserve a memorial, some don't. Probably the memorials are about the tragedies that lead us to reflect on our own mortality, that shake our deepest beliefs, I'm not sure really.
But what is really striking about memorials in the US is that always, without fail, the people remembered are a part of a whole. They left behind family - parents, siblings, spouses, children; friends; relations; probably a documented work of body of some kind. They can be remembered because the rest, humans or deeds, are still alive.
After I visited the Vietnam and Korea War Memorials in Washington DC and uploaded the pictures, a friend wrote back saying, "What about those killed by the soldiers in those faraway lands? If a person was killed and the whole village destroyed (documents proving existence included), there's nobody left to remember. It would be as if they had never existed".
I'm not sure I'd dare to utter these thoughts anywhere near DC, but it's a valid question. I suppose the answer is, beyond a particular event or person, memorials are memory in practice. And that's something that can be started at any point of history.