Thing is, relative compared to what?
Europe was at peace from 1945 to 1989, even though you had two opposing blocs staring each other down straight down the middle. The actual violence was constrained, on the threat of MAD, to proxy wars in non-aligned states. Not exactly peaceful, but not exactly war, either. And you didn't have the concept of the 'failed state', because even states with tenuous and vague institutional systems were propped up generously by either the US or the USSR.
Compare that to what you had after the Soviet Union collapsed. To back what Ezri D and MacLeod have been pointing out, the breakup of Yugoslavia (and the street violence and ultranationalist militias slaughtering people on all sides) occurred just when the idea that a land war in Europe was, to many military and academic minds, unthinkable. (Of course, the violence in Yugoslavia was egged on by the Western 'advisors' and international bodies who wanted to see the last Communist country fall apart, but that's another point...) Somalia broke down. Rwanda ripped itself apart and killed (conservatively) 800,000 people in the process. Afghanistan became, under the joke that was the Peshawar Accord, a proxy-war playground between the Saudis and the Iranians.
What about relative to the entire history of humanity?
The XX century was the most peaceful century in history (followed by the XIX century) - despite the world wars, proxy wars, civil wars, Yugoslavian war, etc.
A far larger part of humanity was at peace in the XX century (XIX century) than at any other time in history.
History is just that war-filled.
For example, at present, we take for granted that wars between developed countries are very rare and that wars mostly happen in third world countries; in reality, that's an absolute novelty.