(Well John, you did say most important invention, not the one we should be most proud of). The invention (and detonation) of the atomic bomb has changed the world more profoundly than any other human development in the last 2000 years. In seconds, nearly 200,000 people were dead or dying in Hiroshima, and consciousness was forever changed on our planet. Although the arms race fueled our economy for a few more decades, the bomb set into motion a 'warfare stalemate'. With the ability to destroy our planet within the realm of possibility, we were forced to examine our rules of war, and seek new means of engagement to work out our differences. And although hundreds of wars are going on at any time on our planet, there are checks and balances, underscored by the horror of Hiroshima and Nagasaki.
Please note that if you were to have phrased the question to include time prior to 2000 years ago, then I would have suggested that our most powerful invention would be song.