The previous post is accurate in that there has been some level of integration that can demonstrate success. The old ideologies that drove the Iron Curtain to descend upon Europe disappeared and in its place was a new paradigm where nations were quickly appropriated into market economies. This was enhanced with globalized economic realities, helping to integrate more of the world as well as Europe. I think that the where this line ends up being moved to is going to be the challenge here. On one hand, the issue of Greece is a sticky one. To what extent does integration play a role in "bailing" out a nation such as Greece? It is difficult to push integration, but then retreat back to protectionist measures when convenient. As many nations are seeking to understand how globalized and integrated economies are impacted in worldwide economic challenges, European nations are no different in trying to understand this new paradigm.
I would say that it has only succeeded to a certain degree. Recent events show us that it is not fully integrated.
I think that you can argue that the EU has integrated to a great degree, especially economically. They have created a common currency and they have so much of a common market that there are essentially no barriers between countries. This is a remarkable achievement.
But the recent problems with Greece show that this integration is not complete. Some countries have much weaker economies and have governments that are much less willing to push for reforms than other governments. When these "lower performing" countries get in trouble, the other countries (notably Germany) do not really want to sacrifice to help them out. This shows that the various countries do not yet see each other as "self." They still think of themselves as different countries and do not want to sacrifice for one another.
This shows that they are not completely integrated.