By pretty much any definition (whether you are talking about declared wars, undeclared conflicts, other uses of armed force, murders, rapes, assaults, other petty crime, total number of people killed violently due to the action of another human being) statistically we are living in the most non-violent times in the history of the mankind. It's been a little while since I've read On Killing but from what I remember Grossman's argument is that we are living in the "most violent times in history" from the standpoint of people being more conditioned to kill, particularly in the developed world, making crime rates and the like go up...but this is statistically untrue as violent crime rates in pretty much every category (murders, rapes, assaults, etc), both in the U.S. specifically and the developed world in general, have been on a steady decline for the past 20+ years (during the same time where the things that Grossman claims are responsible for increasing the conditioning to killing among the general population have been on the rise...violent movies/TV/video games, other popular glorification of violence, etc).
Grossman does a lot of good stuff and has a lot of good and interesting ideas, but his work has some pretty serious methodological flaws, and that's one of them. Another would be that he based his "U.S. soldiers in WWII rarely fired their weapons because they weren't conditioned" thing off of S.L.A. Marshall's work Men Against Fire, and that particular claim has been revealed to be more or less completely made up bullshit on the part of Marshall...but at the time Grossman wrote On Killing Marshall's claim had already been disproven yet Grossman still made it central to his thesis. Ironically enough there is evidence that Marshall specifically included it in Men Against Fire (despite being on very shaky empirical ground) in part to spur Army leadership to institute the very conditioning that they did wind up using, and the type that Grossman talks about.