I don't see that happening ever. Not unless the human condition changes significantly. I currently see it more likely that we will end up with more countries, not less countries.
If countries "go away", what do you suggest they would be replaced by?
50 years ago it was difficult to be a city-state, Monaco couldn't have it's own currency, army , foreign embassies.
Now it would be much easier for eg. Scotland/ Bavaria/ Flemish-Belgium to become a country again - they would have a euroepean central bank/currency/etc but could handle everything else locally instead of in a capital city 100mi away that is only the same 'country' because of a battle 500years ago.
The EU isn't a country though, and it will never be one; different cultures have different values and often don't want to live under the same set of laws. Personally, I think this is a good thing. If you're oppressed under one countries set of laws at least you always have the option of leaving.
If countries "go away", what do you suggest they would be replaced by?