In almost endless ways, we are still dealing with the aftershocks now.
Here are just some of the ways in which the collapse of the USSR affected the world. I am sure others can think of other ways:
A new wave of democracy as old Communist regimes collapsed in Eastern Europe, in particular, and as the US abandoned its support for authoritarian right-wing regimes in Latin America, especially, as the country no longer felt the need to put stopping the USSR ahead of democracy and human rights.
A new focus on democracy and human rights as an outcome of foreign policy, rather than an attempt at containing the Soviets, no matter the cost
The end of wars in places like Angola, where the two sides were essentially proxies for the two superpowers
The US becoming the sole superpower and the creation of a unipolar world (though we are now, arguably, seeing the rise of additional poles)
Independence for ex-Soviet republics such as the Baltic states, Ukraine and the Central Asian Republics such as Kazakhstan
The collapse of the Russian economy, mass-poverty, the rise of gangster capitalism, leading to cynicism of democracy and capitalism, and the eventual rise of Vladimir Putin