If we don't kill ourselves off first it will probably happen eventually. Country sized used to be limited by things like communication latency, and the time it took to move forces around. Technology has shrunk the world so that those things no longer matter. The natural size limit on a country is almost certainly as large as the earth now.
It won't happen soon, cultures will take time to become similar enough to merge. Leadership structures take time to be absorbed into a greater one (EU style) or have to forcefully taken over (Chechnya style, thankfully very rare these days). But with no real impediment to countries growing larger, it will happen eventually. With no-one able to fund or support rebellion and modern technology making police actions extremely effective it may well last effectively forever.
Whether it's a democratic utopia, a dictatorial nightmare, or something in between for the common citizen is not yet defined. Either way, war, as in peer to peer conflict between sovereigns, will be over.