The first point to make is that death totals should be judged in relation to the total population of the world. Twenty million people dying in a century, when only 100 million people lived at all, is much worse than 50 million dying in century in which a 1 billion people lived (This depends on a moral contention that it is worth choosing to live at all).
I shall argue that the 20th century was not in fact the bloodiest century ever. Indeed I'll argue that despite the wars, genocides and created famines of the last century that most of the history of homo sapiens has been worse (again on a per capita basis). Furthermore I shall show that there have been at least two (quite possibly many more) centuries in the last 2000 years which were clearly more bloody than the 20th century.
There are many problems with the statistics for warfare, genocides and famines:
1) Death counts collated by armies or politicians cannot be trusted due to bias and neglect.
2) Counting deaths caused directly by weapons results in a gross underestimate.
The authors of the 2006 Lancet study concerning the Iraq war say "Aside from Bosnia, we can find no conflict situation where passive surveillance recorded more than 20% of the deaths measured by population-based methods".
3) The historical record is poorer the further back in time you go. As a result major famines, genocides and wars in remote parts of the world may have been underestimated or even overlooked.
4) Famines caused by gross mismanagement of the economy or by political suppression are often counted as atrocities when these events occurred in the 20th century. Logically, however, when comparing centuries we must take such famines into account from earlier centuries. It is very hard to find good statistics on human caused famines prior to the 20th century. This may result in an underestimate of our death tolls by as much as a factor of 2.
A cautionary note: Together these problems mean that any casualty estimates by people other than serious historians will almost certainly be underestimates (assuming they don't just quote historians).
I cannot give figures for deaths due to warfare for any century other than the 20th. I have searched the Internet and have been unable to find the necessary data. However, there are other ways to demonstrate my point.
Firstly tribal societies have very high rates of mass male on male violence. See Steven Pinker's excellent article on the history of violence.
The relevant quote "If the wars of the twentieth century had killed the same proportion of the population that die in the wars of a typical tribal society, there would have been two billion deaths..."
The precise figure is debatable but even if its out by a factor of 5 the conclusion still holds: For most of human history we were tribal (or mostly tribal) so most of human history was more bloody than the 20th century was.
Secondly I shall show that the 8th century and the 13th century were both more bloody than the twentieth.
In the 8th Century 36 million people died as a result of a single civil war in China known as the "An Shi Rebellion". Adjusting for world population (210 million) this is almost twice as bad as the death toll for the entire 20th century (I assume a high estimate of 231 millions dying in the 20th century). A comparison based on all the warfare, famines and genocides would almost certainly be much worse.
In the 13th Century 40 million people were killed in various wars that can be grouped under the heading of the "Mongol Conquests". The population of the world had grown to 442 million. Never the less, the figures for this campaign itself are enough to show the 13th century to be more bloody than the 20th.
I am not in a position to answer the question "Which centuries were genuinely more bloody than the 20th century?". However, its obvious that a good statistical analysis would throw up further surprises.
In conclusion there has been progress in reducing the per capita impact of man made mass murder but how fast this is occuring and how steadily is still unclear to me at least (despite my best efforts to find sources).
Finally I should point out that I do not intend to judge past ages using standards from the 21st century. I intend rather to show that being born in the 20th century results in a lower risk of death due to warfare, genocide or engineered famine than being born during most of the rest of the history of man.