Crime never disappears completely, it just "sublimates" itself and becomes active in new "territories". You could say that the modern industrial society is way more secure and crime-free compared to the Dark Middle Ages, just to give an example, after all you can now pretty safely go from one town to the next 20 kilometers away without fear or getting robbed or worse (in most of the world's places, anyway).

But today, unlike 1000 years ago, we're also a couple of button-pushes away from almost total species annihilation (the effects of a a possible nuclear winter are yet to be determined exactly), to say nothing of the countless genocides perpetrated during the 20th century and into the 21st or about the the two world wars.