Does imperialism still exist?
In one sense, imperialism does not exist today. This is the case if we define imperialism as the process where one country actually takes the territory of another country and makes it a part of its own country. There are very few instances of this even being attempted, much less achieved, in recent times. We could perhaps say that Iraq was attempting imperialism when it invaded Kuwait in 1990. Outside of that, there are no instances that I can think of (in at least the last 30 years) in which a country really tried to take another entire country and add it to its own territory.
On the other hand, we can conceive of imperialism a little more loosely and say that it does still exist. If we say that imperialism occurs when a country uses its military, political, and economic power to extend its power and influence, then imperialism happens all the time. By this definition, the US is an imperial power. Our use of military power to oust Saddam Hussein and replace him with a more friendly government and our efforts in Afghanistan today would be seen as imperialism. Chinese efforts to use their economic power to gain influence in Africa and other places would be imperialism as well.
All in all, then, it seems that the older, more blatant form of imperialism is dead but that there is still imperialism of a different sort today.