Around 25 percent of Americans want their state to secede (1). A lot of Italians want Northern Italy to part with Southern Italy. Spain has Catalan and Basque separatists. The UK has Scotland, and perhaps even Northern Ireland.
There are many people in many places that think they would be better off in a more (formally) independent state.
For now, the EU skeptics are a small minority in most EU countries. I for one hope it stays like that. The EU has shown remarkable unity when met with Brexit.
1: http://blogs.reuters.com/jamesrgaines/2014/09/19/one-in-four...