I read this claim somewhere recently, and a google search shows that it's occasionally made around the web, but was perhaps more common in the 1970's (many of the stories I find online are people reminiscing over old protests).
At first glance it seems probable to me: wars historically haven't killed all that many people (mostly because there were not all that many to be killed). In the US alone, wikipedia gives a figure of about 40,000 deaths due to motor vehicle accidents this year. Assuming that the US death rate is a reasonable estimator for the world (assuming poor countries have fewer cars, but more accidents), I get the total figure should be 40,000*20 = 800,000 this year alone. The accident rates were actually higher in the past, although population was lower, so my first guess is that we had ~10 million deaths in the last 15 years, and probably another 15 million or so in the 10-15 years before that. My guess is that overall deaths are probably something like 45 million, but this might be off by +/- 15 million.
My guestimate for war is that WWI and WWII combined saw about 40,000,000 deaths, so that gets us into the same ballpark.
What I'd really like to see is an authoritative source on the total figures for both types of death, and maybe something on the origin of the claim. Can't seem to find either. Might also be interesting to see if/when this will become true.