The OP is mistaken and like many people think the EU is some kind of antagonistic entity that was forced upon their country, whereas in reality the EU has been funded by its member states as a voluntary union of members states - by unanimous votes, in all important matters. Every feature of the EU is the result of careful, decade long discussion between the governments of members states from all kinds of political sides.
The reason why the EU is perceived so bad in some countries (like the UK) are partly historic and partly because it the EU is the perfect scapegoat for local politicians who have messed things up. In the UK, scapegoating the EU for your own mistakes was particularly common.
Add to this the facts that the Leave campaign lied about practically everything - or at least intentionally distorted the facts - and that many voters don't know much about the structure of the EU, and the Brexit became reality.
It is unlikely that a similar decision will be made in any of the remaining 27 countries, for lack of popular support and because people there are more aware of the benefits of the EU. Never say no, though, fuelled with money from outside the EU, currently right-wing populists are pretty good at exploiting the fact that the divide between the rich and the poor is ever increasing very cleverly, and since poverty will increase in all EU countries, irrational and populist recipes for "the simple man on the street" can continue to gain in popularity. Radical left wing parties have largely the same agenda, so these are interchangeable.
So it's possible that one or two countries might attempt to exit the EU after some populist party has won an election. It's unlikely, though, because the EU offers overall way more benefits than disadvantages. It's budget is ridiculously cheap in terms of percentage of GDP and you get a lot of bang for the bucks out of the trade union alone. Moreover, future generations are fairly pro-EU in most member countries (though there are some outliers).