I've thought talk of the EU breaking up to be too unrealistic, but no one can deny the EU is in trouble. Why do countries keep joining it?
Look at the countries that wish to join (Croatia, Serbia, Albania) and the countries that have in recent years backed away from membership talks (Switzerland, Norway) and you've got your answer. The EU still offers a lot of incentives for the smaller and poorer countries of EEurope thanks to the cohesion funds + it's still seen as a sign of progress to be inside of the EU in these places.
Politicus have already covered Iceland.
So let us look at the two others.
Norway have attempted to join 3 times, everytime there was a no in the referendrum, big surprise that they don't try to join again, while having a booming economy build on oil.
Switzerland will never join, it would be a pure nightmare for Switzerland to win all the refrendrum in the cantons needed to join, and economical it would demand that Switzerland changed a lot of the parasitic behaviour which make them rich.