The number of Indians who died at the hands of the European invaders is highly debatable, and it basically centers on two questions:
Pick a number, any number.
Sometimes it seems that this is the way historians decide how many Indians lived in the Americas before the European Contact. As The New York Public Library American History Desk Reference puts it, "Estimates of the Native American population of the Americas, all completely unscientific, range from 15 to 60 million." And even this cynical assessment is wrong. The estimates range from 8 to 145 million.
If you want to study the question of pre-Columbian population and its subsequent decline in detail, two good books to start with are David Henige, Numbers From Nowhere (1998) and Russell Thornton, American Indian Holocaust and Survival (1987).
Population of the Western Hemisphere in 1492 according to various experts:

The problem, of course, is that by the time that the Europeans got around to counting the Indians, there were a lot fewer to count
I've graphed the estimates chronlogically to show that the passage of time and the gathering of more information is still not leading toward a consensus. Over the past 75 years, estimates have bounced around wildly and ended up right back where they started -- around 40 million.
I've also graphed the population of Europe in 1500 because this is magic number to which many of the estimates aspire. Native American history is traditionally treated as marginal -- a handful of primitive kingdoms that were easily overwhelmed by the most dynamic civilization on Earth -- but if it could somehow be proven that the Americas had even more people than Europe, then history would be turned upside down. The European conquest could be treated as the tail wagging the dog, like the Barbarian invasions of Rome, a small fringe of savages decending on the civilized world, wiping out or enslaving the bulk of humanity.
The advocates of large numbers, however, are often their own worst enemies. On page 33 of American Holocaust, David Stannard declares, "[P]robably about 25,000,000 people, or about seven times the number living in all of England, were residing in and around the great Valley of Mexico at the time of Columbus's arrival in the New World".
Now, I've been to England, and I can vouch that the English have left their mark on the land. You can't throw a brick in England without hitting some relic of the earlier inhabitants -- castles, cathedrals, Roman walls and roads, Stonehenge, etc. -- not to mention books, tools, coins, weapons and all the little pieces of the past that turn up anytime someone plows a field or cleans their attic.
Now go back and read what Stannard has written. I'm sure that the point that he's trying to make is that since there were seven times as many Mexicans as English, truly the Mexicans were seven times more civilized than the English, so if anyone deserved to be called "savages", it's the English. Unfortunately, the point that nags at me is "If there were seven times as many people in Mexico, shouldn't there be seven times as many relics in Mexico?" Yes, I've read the archaeological reports that discuss irrigation systems, and I've seen the big, colorful picture books showing jungle-encrusted ruins of ancient pyramids, but the fact is that seven times the population of England should have left behind a lot more stuff than that.
I find the estimates for Virginia even more awkward because I live here. Stannard estimates the population of Powhatan's Confederation at 100,000, yet there's not a single site in the Virginia Tidewater that remotely hints at the complex infrastructure necessary to support even half this number. There's not one ruin of any permanent building. Artifacts of any kind are rare -- barely even a single burial mound worth pilfering. And it's not like there's some forgotten ghost town deep in the desert or jungle waiting to be discovered. This is Virginia. It's been settled, plowed and excavated for 400 years.
I also find it difficult to believe that the Europeans obliterated all traces of the earlier inhabitants. After all, I've been to Germany too. I've seen that bombed-out cities still have a substantial presence of the past, and I doubt that the conquistadores could be more destructive than a flock of B-17s. [n.3]
In any case, the median of all the estimates charted above is 40 million. It's the type of number that half the experts would consider impossibly big, and the other half would consider impossibly low, so it's probably exactly right.
And then, within a century of the European Contact, the hemispheric population plunged to a fairly well-proven residue of less than 10 million. How many of these deaths count as indictable atrocities?
In American Holocaust, Stannard estimates the total cost of the near-extermination of the American Indians as 100,000,000.
The problem here (aside from the question of whether there were even this many people in hemisphere at all) is that Stannard doesn't differentiate between death by massacre and death by disease. He blames the Europeans for bringing new diseases which spread like wildfire -- often faster than than the Europeans themselves -- and depopulated the continent. Since no one disputes the fact that most of the native deaths were caused by alien diseases to which they had never developed immunity, the simple question of categorization is vital.
Traditionally we add death by disease and famine into the total cost of wars and massacres (Anne Frank, after all, died of typhus, not Zyklon-B, but she's still a victim of the Holocaust) so I don't see any problem with doing the same with the American genocides, provided that the deaths occurred after their society had already been disrupted by direct European hostility. If a tribe was enslaved or driven off its lands, the associated increase in deaths by disease would definitely count toward the atrocity (The chain of events which reduced the Indian population of California from 85,000 in 1852 to 18,000 in 1890 certainly counts regardless of the exact agent of death, because by this time, the Indians were being hunted down from one end of California to another.); however, if a tribe was merely sneezed on by the wrong person at first contact, it should not count.
Consider the Powhatans of Virginia. As I mentioned earlier, Stannard cites estimates that the population was 100,000 before contact. In the same paragraph, he states that European depredations and disease had reduced this population to a mere 14,000 by the time the English settled Jamestown in 1607. Now, come on; should we really blame the English for 86,000 deaths that occured before they even arrived? Sure, he hints at pre-Jamestown "depredations", but he doesn't actually list any. As far as I can tell, the handful of European ventures into the Chesapeake region before 1607 were too small to do much depredating, and in what conflicts there were, the Europeans often got the worst of it. [see http://www.mariner.org/baylink/span.html and http://www.nps.gov/fora/roanokerev.htm and http://coastalguide.com/packet/lostcolony01.htm]
Think of it this way: if the Europeans had arrived with the most benign intentions and behaved like perfect guests, or for that matter, if Aztec sailors had been the ones to discover Europe instead of vice versa, then the Indians would still have been exposed to unfamiliar diseases and the population would still have been scythed by massive epidemics, but we'd just lump it into the same category as the Black Death, i.e. bad luck. (Curiously, the Black Death was brought to Europe by the Mongols. Should we blame them for it? And while we're tossing blame around willy-nilly, aren't the Native Americans responsible for introducing tobacco to the world -- and for the 90 million deaths which followed?)
I can't confidently estimate the number of unnatural deaths (i.e. indictable killings, as a result of violence and oppression, both direct [war, murder, execution] and indirect [famine, avoidable disease]) among Amerindians across the centuries, but as a guess, I'd say 20 million, for no reasons other than it's half of the original 40M, and it seems to be near the median of the 4 previous estimates. (Rummel, Barrett, Althea, Stannard)
Not the most solid grounds, I'll grant you.