Yes, I think that the European Union should continue to remain united. As an economic and political organization, it has done quite well -- with one or two exceptions. What they should start doing, however, is become more selective about who they let into the Union. Not all applicants share the EU's ideals of human rights and economy.
Without the European Union, Europe would cease to coexist peacefully the way it does today. True, Greece's bankruptcy problems and the overall global financial crisis has raised tension amongst the EU nations, but in the end, the Euro has been a huge success and the travel abilities throughout the entire continent is still an increidlby popular thing.
I believe the E.U. should remain united. If it doesn't remain united I think the main purpose is lost. The main purpose is to unite under one set of standards not break up and create two different sides. If the E.U. can't operate as a sole unit then they shouldn't operate at all.
The EU should remain united and show strong solidarity in order to have the most long lasting success. There will always be disagreements between member nations but they need to be worked out and continue on with their relationships. The nations need to compromise and serve good policies that will benefit all their nations.
Yes, the European Union should remain united, because a lot of things got a lot easier when the EU because United. The most obvious example is with money. Travelers no longer need to order 5 currencies or more, just to make a trip across Europe. Immigration is also simplified in a centralized system.